Adjust handlebar position/height (damaged screw?)
If you find that it can't be fixed, then try to go with a solid stem that's already at the correct angle. I had an adjustable one before and after adjusting it, I could never get it to be tightened properly and it would always wobble.

A bike co-op or bike dump is a good place to look for parts like this as solid stems don't usually wear out and many of them are salvaged from old bikes that may no longer be usable.

Now that I think of it, I'm pretty sure the nut was rounded off similar to yours after many tries to remove the wobble. The adjustable  ones are usually low quality because they are heavier than solid stems, and people who buy more expensive bikes don't mind spending a few extra dollars to get a good fit.