The 53-year-old entered a guilty plea to one charge of using threatening or abusive behaviour when he appeared at Edinburgh Sheriff Court. The charge related to an incident at Edinburgh Airport on May 19 last year.
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 apologised to 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 Edinburgh, and realised later that he had left his phone on board, the court heard.
He asked baggage handlers for help but became abusive when they asked for flight details.
Police officers became involved but he continued to hurl insults, repeatedly calling 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".
The sheriff added: "At least you have taken this opportunity to apologise."
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 colleagues in a House of Commons bar in 2012.
The former Army major was fined £3000 and banned from pubs for three months following the brawl in the Strangers' Bar.
Joyce arrived at Westminster in 2000 shortly after quitting the Army, making claims of snobbery, sexism and racism in the armed forces. He was elected as Labour MP for Falkirk West in a by-election before increasing his majority in the General Elections of 2001 and 2005, which he held by a comfortable margin in 2010.