Fig began playing drums at the age of four. After performing in numerous successful local rock bands in Cape Town, becoming locally respected with bands like Hammak, he moved to Boston to further pursue his musical interests. His formal education included studies at the New England Conservatory of Music in Boston, where he studied jazz and classical disciplines, and graduated with honors in 1975. In 1976, he moved to New York City, where he began to establish a career as a freelance musician. Fig was a member of the band Spider during both their album releases in 1980 and 1981 as well as on their 1982 album as newly-renamed band Shanghai, together with famed producer Beau Hill and songwriter Holly Knight. Fig had been the drummer on Ace Frehley's 1978 solo album and subsequently became a member of the then ex-Kiss lead guitarist's solo project Frehley's Comet from 1984 to 1987. Fig also played drums on all but one song on Kiss's 1979 album Dynasty and every song on their 1980 album Unmasked; the bringing-in of Fig to replace usual drummer Peter Criss upset Criss, to the point where, after appearing in promotional videos and tours through Unmasked, he left the band. Eric Carr took over drumming duties following Criss's departure. Other artists with whom he has worked include Bob Dylan, Warren Zevon, B. B. King, Peter Frampton, Joan Armatrading, Cyndi Lauper, Link Wray, John Waite, Robert Gordon, Eric Johnson, Joe Bonamassa, Beth Hart and Kix.
Some of the many recordings Fig has made include selections with Bob Dylan, Mick Jagger, Cyndi Lauper, Madonna, Gary Moore, Shanghai, Ace Frehley, Joan Armatrading, Rosanne Cash, Joe Cocker, John Phillips, Warren Zevon, Sebastian Bach, Oz Noy, Jed Davis, Joe Satriani, Paul Butterfield, and Chris Spedding. He replaced Peter Criss on the Kiss albums Dynasty and Unmasked, playing drums on all tracks for both albums. Due to Kiss' management attempting to cover up any personnel problems within the band, Fig would not be credited until years later, and Criss appears in the video for "Shandi" off the Unmasked album. As a freelance drummer, Fig has also played live with Paul Simon, Booker T and the MG's, The Thompson Twins at Live Aid, and Jim Keltner for Bob Dylan's 30th anniversary concert celebration. In 1996, Fig released a drum instructional video and book titled In the Groove and Late Night Drumming, respectively. In 2002, Fig completed his first solo record, Figments. Produced and co-written by Fig, the record represents three years of work and includes - among others singers and musicians - Richie Havens, Brian Wilson, Ivan Neville, Sebastian Bach, Ace Frehley, Al Kooper, Chris Spedding, Donald 'Duck' Dunn, Blondie Chaplin, Paul Shaffer, Chris Botti, Randy Brecker, and Richard Bona. In 2006, Fig worked with Blackmore's Night on The Village Lanterne. In 2007, Fig worked with Joe Bonamassa on his Sloe Gin album, in 2009 on his Ballad of John Henry album, and in 2014 on Different Shades of Blue. On 4 May 2009, Anton joined Joe Bonamassa's band for their debut appearance at the Royal Albert Hall in London, where Eric Clapton made a guest appearance. A DVD capturing this performance was subsequently released. Fig was featured on Ace Frehley's album Anomaly, released on 15 September 2009.