yeah there is no problem in doing so, you just need to make sure the phone is not sim locked, if yo got it directly through your carrier then it will be, if you got it from phones for you / carphone warehouse it probably isnt, if it is locked contact your provider and ask for the unlock code, or have a hunt online for companies providing this service. (all at a cost)
one thing to remember when using the ST&T Sim make sure its got data in as a bundle otherwise your bill could get HIGH through their PAYG sim.