Sloma started his career at Wimbledon, where he captained their youth team. Whilst on the books at Wimbledon, he was loaned out to Hampton & Richmond in December 2001.|
The versatile left sided player then joined Aylesbury United and made his debut in August 2002. Sloma made 18 appearances in all competitions for The Ducks, playing his last game in November 2002.
Sam then joined Wingate & Finchley where he stayed for four seasons, making a total of 167 appearances scoring 34 goals in all competitions.
Whilst at Wingate, Sloma represented Great Britain at the 2005 Maccabiah Games, dubbed ‘The Jewish Olympics’. He also had a short stint in the USA with A-League outfit, Milwaukee Waves.
Ryman Premier club, Wealdstone signed Sam in February 2006, before joining Conference South, Thurrock two months later in April 2006 on a dual registration with The Stones.
In June 2006, Sloma joined Dagenham & Redbridge helping them to achieve Football League status for the first time in their history and scored their first ever football league goal.
After their first season in the League, Sloma was released from the Daggers along with former Grays player, Dave Rainford, claiming the style of play no longer suited him.
Subsequently the 25-year-old signed for Grays Ath in June 2008, despite interest from a number of other League and Conference clubs.