The UK Immigration Rules for Visitors state, in relevant part:
V 3.1 This Part applies to all applications for visit visas, leave to enter, and an extension of stay as a visitor except where explicitly stated otherwise.
(As a US citizen, you do not require a visit visa in advance; under the UK immigration rules you will apply for leave to enter by presenting your passport at the UK Border at the airport.)
V 3.4 An application (except for an application for an extension of stay as a visitor) will be refused if the applicant has been convicted of a criminal offence for which they have been sentenced to a period of imprisonment of:
(a) at least 4 years; or
(b) between 12 months and 4 years, unless at least 10 years have passed since the end of the sentence; or
(c) less than 12 months, unless at least 5 years has passed since the end of the sentence.
Where this paragraph applies, it will only be in exceptional circumstances that the public interest in maintaining refusal will be outweighed by compelling factors.