yes, you can very well go in for orthodontic correction of your upper front teeth, adult orthodontics is gaining momentum now and its highly successful ,in correction of aesthetics and function. i advice you to consult an orthodontists( specialist in correction of mal alignment of teeth), he would advice you for an opg ( radiograph) and would also , educate you about the various techniques by which correction is possible ( metallic braces, ceramic braces, invisible braces etc). alternatively if you donot wish for an elaborate orthodontic correction which seems to be the best way to treat your case, you can also ask for crowns.