I WANT TO BE A AMERICAN :( LOL?

Can u become a American citizen with a criminal record I plan on doing a degree next year and I can only presume this will help the record is for ABH (actual bodily harm) i think this is the lowest ualt charge u can get in the uk and I have a spent theft charge. I also read some where that u can apply to get a conviction remove I'm not sure if this was just in the eyes of the American government or not I'm from the uk