Nope. In the U.S., registration is different from voting. Registration, which occurs before elections (or sometimes contemporaneously), is the process by which one proves one's eligibility to vote, including citizenship, residence within the district and precinct, and lack of disqualifiers such as a felony conviction. This is often accomplished by "motor voter," in which one registers at the same time one gets one's driving license.
On election day, one goes to the polls, where they have the electoral rolls listing all registered voters. One gives one's name, and it is checked against the electoral rolls. The ONLY thing one is asserting at the polls is that one is the person listed in the rolls, not that one is eligible to vote in that district and precinct.
I would suggest that if one is worried about the non-existent problem of "voter fraud," any state-issued or Federal-issued (such as a military ID) picture ID card would satisfy the requirement of demonstrating that one is, indeed, the person whose name is listed on the electoral roll. But Texas and several other states have decided to pick and choose which forms of ID are acceptable, presumably because they seek to suppress the votes of people in groups that skew Democratic.