If you're gunning it, its called torque steer. Along with that torque steer too, like Chad said, you probably need an alignment. I dont know what to tell you though. If you abuse a car, even a Toyota, it still cant always hold up. Take it to a mechanic and pray its not something serious. Be careful too, because I know a lot of dealerships are stingy about things, and if they could tell youve raced in the slightest, theyll F you hard core!
what kind of tires do you have?? mine is doing the same thing. I have had it aligned and rechecked twice. Today my tire place told me I had a bad tire (only 200 miles on it). I have 205/40/17's, directional tires. I think my box does not like the tread design of the tire. I am trying to find some old non-directional's to try. When I put my stock 15's on, I have no problem.
Tundra solutions.com has a knowledge base with TSB's from Toyota in it. You have to be a member to read them. If you can find someone who is a member, go the STEERING section and get the ST005-01 TSB. It is a bulletin put out by Toyota addressing the pulling problem. Turns out I had bought a set of el cheapo tires and they had a "conicity" problem, causing my box to pull to the right. I put a new set of Fuzion's on the front and it fixed the problem.
i wouldnt really reccommend driving and letting go of the steering wheel. cars are meant to be driven with both hands on the wheel, usually when diagnosing a pulling/alignment/tirewear problem, you should drive with the steering wheel straight ahead, and see where the car goes. if you go straight with the steering wheel crooked probably have a out of spec. Toe adjustment, if it is straight and kinda wanders, check tires.