There are several options as to why she might be wiggly like this. I'll be happy to help you walk through and troubleshoot if you'd like.
are naturally movers and wigglers and just won't settle. Girls tend to be more this way than boys. If this is her personality, then when you are sitting with her and playing with her, she isn't going to want to be held in one place, so she'll squirm free and go about her busy rat playing.
Every rat I've ever owned scratches. It's a side effect of being a small climbing critter with sharp claws that don't retract. Some do it more than others depending on their excitability or fearfulness. To cut down on scratches, I've got a long sleeve hoodie shirt I wear that is my dedicated 'rat shirt'. It never gets washed and I only wear it when I'm playing with the fur kids. Another advantage of that shirt is it smells like my rats. Rats use scent to determine what's theirs and what's safe. So my rats feel more comfortable coming to me when I'm in the shirt than when I don't wear it. It also has the advantage of providing a hidey place with the hood.
Another possibility to look at is the way you pick her up and hold her. For example, do you have to chase her in her cage to pick her up? If you do, when you corner her do you grab her firmly from above? If this is what happens, then yes, this might be one of the problems.
Because rats are prey species, they are conditioned to fear anything that chases them or grabs them from above like a hawk swooping down on them.
If you have to pick them up by hand then ideally you approach them calmly with both hands held low to the sides of their body so they can see your hands coming. Talking to them as you do this also helps. Then scoop them up from beneath. I've found that if they're skittish, I gently maneuver them to a corner (not chase), and as I'm scooping underneath, I thread one hand around their backside to keep them from backing out of my grasp. While the other gently threads around their shoulders and ribs. Then I pull them close to my body and step away from the cage because often if they're skittish, they will immediately squirm loose and jump back to the cage. I never grip them hard, just adjust my hold as they move. As I step from the cage, I usually open my grasp and let them climb to my shoulders or hoodie if they prefer. If I'm away from the cage, they realize that the safest place is my arms or shoulders.
If they immediately try to climb down my body like one of my girls used to do, I don't hold still, I just keep walking to the designated safe play area. The movement throws off their balance just a nudge so they don't feel as comfortable scooting down my body. Then I kneel down, offering them an arm to run down and get on the floor/bed/whatever. This is all assuming that your rat is basically comfortable with you.
If you are holding a rat while walking and they're still trying to bolt from you, then you know they are absolutely terrified, because they are willing to risk bodily injury in a five foot fall to get away from the big scary human.
In that case, carrying them around isn't what you want to do yet. You need to back up the taming
process and work on getting them completely comfortable with your presence (which we can give you tips on if needed).
With my rats, they ride on my shoulder or in the hood of my hoodie unless there's physical issues that make it safer for me hold them in my arms for security--for example my old man Tucker was too frail to be safe on my shoulder.
I do a lot of my bonding/taming work in a designated play area. Small and barren enough that they feel obligated to come back and interact with me in some way, be it by climbing on me, taking treats from me, or just hanging out on me while I read to them. I love reading as a pastime and I feel goofy talking to them constantly as I'm not a naturally verbal person, so by reading out loud we both benefit.
It may just be that your girl is not a lap rat. Most of my girls don't like being held. My hairless boys-very much like girls in temperament- don't like being held. They all just love moving too much. My big black boy likes it, and so do two of my lazier girls. They all love coming up to me on their own and getting the occasional scritch and they'll often come and lounge on my body as long as I don't restrain them.
I'm sure you've dealt with all of the above that I've gone over and may even be saying 'yes yes, I already know this, but how do I get her to let me hold her'. But, the main point to take away is to give the rat a choice while insisting on contact with them. Rats are xenophobes who take a long time to develop trust, and who don't like being forced. If it becomes their choice to have contact with you, or if they don't feel like they are forced they'll warm up to you much better. All of my tips-- no chasing, minimal grasping, being allowed freedom to move over your body or ride on your shoulder while being held or carried, respecting that they just may not be lap rats, but instead explorer rats-- help build trust and strengthen your bond. That is what will increase the chances that she will become comfortable hanging out as a lap rat, or at least helping you understand her needs if she doesn't.
I wanted lap rats when I first looked at getting rats, so I got boys. As boys mature they get lazier and lazier, and are often content with hanging out with you by the hour. If you did decided to get a boy, you will want to get him neutered to prevent accidental litters which will happen in the blink of an eye no matter how careful you are. When I got girls, I neutered all of my boys. You would also want to do Rat Introductions so that he and your girl learn to know each other in a neutral location, otherwise they may kill each other over territory disputes. Intros involves a specific process, so if you ever decide to get another rat, research that, or ask us and we'll be happy to give you tips. Getting a second rat will also have the added benefit of giving her company when you can't spend time with her.
Let us know if any of this helps or if I'm missing anything.