which category of visa are you planning to apply for? if you are applying for a non-immigrant visa, which category are you planning to apply under? student? au pair? something else?
http://london.usembassy.gov/cons_new/visa/niv/ index.html
Getting a visa is a lot more complicated than travelling under visa waiver, necessitating an interview at the embassy in london, and usually a job offer from a us company/employer (even for non immigrant)
Have a look on the above link and you'll see how difficult it is. Moving onto immigrant visas, you have virtually zero hope, unless you are david beckham or are married to a us citizen.
In summary, it is very very tricky to get a visa for a longer stay than 90 days, and thats even with no arrests, so factor in your arrest and it might be very hard indeed. The only way you will find out is to apply, but you are pretty much scuppered if they refuse on grounds of your arrest because then you wont even be able to travel there AT ALL