In the US it differ from state to state if you will get DUI when cycling drunk. There are no clear cut answer if cycling drunk is legal or illegal in the US since laws from state to state have different interpretation of the DUI law. "A person is guilty of driving under the influence of intoxicating liquor or any drug if the person drives a vehicle within this state." So different states have different interpretation to the word "vehicle." In Ohio, Florida, and Washington the defined vehicle as "every device capable of being moved upon a public highway and in, upon, or by which any person or property is or may be transported or drawn upon a public highway, including bicycles." So if you got caught by a cop while cycling drunk they may still be able to charge you with public drunkenness or reckless driving.
In Hungary they had a decree that clearly allows cyclists to ride their bike while drunk on major roads despite the dangers that it may pose to pedestrian and the driving public. Hungary has strict laws on drunk driving and they fine you heavily. The Hungary government published on their official gazette signed by Prime Minister Viktor Orban allowing cycling under the influence of alcohol regardless of the level of intoxication as long as the cyclist is capable of steering.