US immigration authorities have no direct access to any criminal records, other than those of the USA and Canada. They would not know about your conviction unless the Irish authorities had passed the information on. Unless you're regarded as a terrorist suspect or a potential drug smuggler, this won't have happened. So you should be able to enter the USA under the Visa Waiver Program.
If you're still worried, and decide to apply for a visa, you need to be aware that the process can take several months. (The current estimated wait,
after attending an interview, is 8 weeks). For much of that time you would be effectively prohibited from travelling outside of the UK and Ireland, because your passport would be held by the US authorities. Further information is here:
http://london.usembassy.gov/nireland/nivisa.ht ml
Chris