We've been texting for a week and he hasn't asked me out. What gives?

A week of messages shows that you have been texting; it does not establish whether either of you wants to meet. If no invitation has been made, that practical question is still open.

You can propose a meeting yourself if that is what you want. A yes with an agreed time, a no, or continued uncertainty gives you different information about the next step, without revealing a whole personality or hidden motive.