The 53-year-old entered a guilty plea to one charge when he appeared at Edinburgh Sheriff Court today.
The charge related to an incident at Edinburgh Airport on May 19 2013.
Speaking outside court, Joyce said he would "reflect" on whether to continue as an MP until 2015.
He said: "My instinct is to stay but I don't know how I will feel in a few days."
Joyce also apologised to the airport staff, police and his constituents.
"I am very embarrassed that this has happened," he said.
"My constituents have seen this before, so they might think other apologies are not meant, but they are."
Asked if he had a problem with alcohol, Joyce said he had addressed such issues.
"I think I am well past that now," he said.
Joyce had been drinking on an evening flight from Heathrow to the Scottish capital, realising later that he left his phone on board, the court heard.
He asked airport baggage handlers for help but became abusive when they asked for flight details.
Police officers became involved but he continued to hurl insults.
Joyce repeatedly called a baggage handler and officers "fat, f****** w******" and goaded officers to "f****** arrest me".
He also referred to an officer of Afro-Caribbean origin as "f****** fat and black".
Joyce began to "flail his arms" when one officer attempted to put him in handcuffs, and he continued to resist until he was restrained on the floor.
Sheriff Frank Crowe described his actions as a "deeply unfortunate, prolonged, drink-fuelled rant".
"At least you have taken this opportunity to apologise," the sheriff said.
As well as imposing a fine, the sheriff ordered Joyce to pay £100 compensation to airport staff and £50 to the police officer he racially insulted.
Defence lawyer Euan Gosney said Joyce was in a "high state of anxiety" because of the recent death of his brother and previous trouble with police.
"He accepts that he allowed this baggage to get on top of him, to get the better of him," he said,
"When he was faced with what he perceived to be a lack of assistance, he allowed himself to become emotional, to overreact, to become abusive."
Mr Gosney, who said Joyce does not intend to seek re-election, added: "A conviction of this nature will inevitably make a return to any form of public life difficult, if not impossible."
Joyce became an independent MP after he was expelled from the Labour Party following his conviction for assaulting politicians in a House of Commons bar in 2012.
The former Army major was fined £3,000 and banned from pubs for three months following the brawl in the Strangers' Bar.
Joyce's arrival at Westminster in 2000 came shortly after he quit the Army, making claims of snobbery, sexism and racism in the armed forces.
He was elected to Parliament as Labour MP for Falkirk West in a by-election.
He increased his majority in the general elections of 2001 and 2005 when the constituency was renamed Falkirk after constituency changes, and held on by a comfortable margin in 2010.