The WYLTIWLT Method - Avoid the Complication of the "Who"

Other answers suggest that you should be consistent with the tone of they rest of your site, but your problem isn't about tone, it's about grammar. If you decide to use the "Sign me up" verison, referring to the "who" of the interaction, and try to be consistent with that everywhere in your site, you're going to run into issues at some point.

"Would you like to?/I would like to" is excellent practical way of avoiding the grammitacal inconsistencies of the type you are concerned about.

WYLTIWLT is pronounced wilty wilt and is proposed in the excellent UX Booth article about the Grammar of Interactivity.

The essential problem is how to deal with the "who" of the interaction, and the WYLTIWLT method solves it like this:

For any label, ask if it fits on the end of question/statement: "Would you like to?/I would like to".

In your case, Sign Me Up Vs Sign Up:

Would you like to sign me up? I would like to sign me up Doesn't work.

Would you like to sign up? I would like to sign up. Works!

I use this all the time and it works a treat.

The WYLTIWLT Method - Avoid the Complication of the "Who"

Other answers suggest that you should be consistent with the tone of they rest of your site, but your problem isn't about tone, it's about grammar. If you decide to use the "Sign me up" verison, referring to the "who" of the interaction, and try to be consistent with that everywhere in your site, you're going to run into issues at some point.

"Would you like to?/I would like to" is excellent practical way of avoiding the grammitacal inconsistencies of the type you are concerned about.

WYLTIWLT is pronounced wilty wilt and is proposed in the excellent UX Booth article about the Grammar of Interactivity.

The essential problem is how to deal with the "who" of the interaction, and the WYLTIWLT method solves it like this:

For any label, ask if it fits on the end of question/statement: "Would you like to?/I would like to".

In your case, Sign Me Up Vs Sign Up:

Would you like to sign me up? I would like to sign me up Doesn't work.

Would you like to sign up? I would like to sign up. Works!

I use this all the time and it works a treat.