The Everton forward was stopped by police when driving a woman’s black Volkswagen Beetle at 2:00 am (0100 GMT) on September 1, while his pregnant wife and their three sons were on holiday.
Stockport Magistrates’ Court in the northwest of England heard Rooney was almost three times over the legal drink-drive limit. A breathalyser test showed his alcohol level was 104 microgrammes in 100 millilitres of breath.
The drink-drive limit in England and Wales is 35 microgrammes per 100 millilitres of breath.
Rooney apologised for his “unforgivable lack of judgement” after his guilty plea.
“Following today’s court hearing I want publicly to apologise for my unforgivable lack of judgement in driving while over the legal limit. It was completely wrong,” he said in a statement.
“I have already said sorry to my family, my manager and chairman and everyone at Everton FC. Now I want to apologise to all the fans and everyone else who has followed and supported me throughout my career.
“Of course I accept the sentence of the court and hope that I can make some amends through my community service.”
Rooney’s legal team asked the judge to consider not imposing a community order because of his ongoing charitable work.
However, the judge said he was “not convinced” that imposing a large fine “would have the same effect”.
Earlier, Rooney, 31, made no comment as he was confronted by a media scrum outside the court.
Wearing a blue suit with his hands in his pockets, he walked into the court building accompanied by a small entourage.
He has been married to his high-school sweetheart Coleen since 2008 and they are expecting their fourth child.
Everton manager Ronald Koeman said earlier this month the matter would be dealt with “internally”.
Rooney was given a warm welcome at Old Trafford on his return to former club Manchester United on Sunday but it ended in disappointment with a 4-0 defeat for Everton.
Rooney, England and Manchester United’s record goalscorer, made a successful start to his second Everton spell following his return to the club from United in the summer, scoring on his first two Premier League appearances.
His form moved England manager Gareth Southgate to offer him an international recall, but he decided to call time on his England career.
Everton are currently 18th in the Premier League after three successive defeats.
Rooney first burst onto the scene aged just 16 at Everton and went on to score 17 goals in 77 appearances for the “Toffees” before moving to Manchester United, where he won multiple trophies, including the Champions League.