Can I get my ID in Texas with a warrant for my arrest

Probably not.

This question comes up frequently here. If the warrant is vehicle or driver related, unless the motor vehicles dept. is completely inept- they will pick up on it.
Calling the DMV to ask could be dangerous to your freedom I guess. I guess you could have a friend call DMV (be prepared to wait a while in most areas) and ask a general question about how warrants are handled without breaking any laws.