What can be done for wrongful accusation of identity theft?

It's not clear what exactly what your sister was charged with, but making a false statement to obtain credit or using someone else's credit card can be felony offenses in the State of Texas, carrying the possibility of jail or prison time. She needs to speak to a criminal defense attorney as soon as possible. She should seriously consider not speaking any further with the investigators until she speaks with a defense attorney.

Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.