(2-part post):
According to the rules on the US Embassy website, anyone who has ever been arrested (even if they were totally innocent of any offence) or convicted for a criminal offence is ineligible to enter the USA under the Visa Waiver Program (using an ESTA). They must apply for a visa. (The process involves applying to the Association of Chief Police Officers and attending an interview at the US Embassy in London).
The USA does not recognise the UK's Rehabilitation of Offenders Act so, for their purposes, convictions never become 'spent'. The US Immigration and Nationality Act states that anyone who has ever been convicted of an offence of 'moral turpitude' is ineligible for entry to the USA. Theft is classed as moral turpitude. (There's an exemption from inadmissibility if the offence was convicted by a person under 18 more than 5 years ago). So (unless that exemption applies) the US Embassy must, in the first instance, refuse to issue a visa. (They have no choice. It's written into US law). However the matter can then be forwarded to Washington as an application for a 'waiver of ineligibility'.