What do you mean, like being shy? No. Of course it's not cute. It's weird. If you're "awkward" and can't look someone in the eye during a conversation or if you are still in a "shy" phase then that's just strange and you probably have social anxiety or something.
Nope. I'm awkward but people find me cute doing all those nervous and shaky stuff because I'm goodlooking. No one's gonna find awkward and ugly as cute.