Sloma started out as a trainee with Wimbledon, where he captained their youth side, before being loaned out to Hampton & Richmond Borough. He then signed for Aylesbury United, making a total of 18 appearances, before moving on to Wingate & Finchley.
Sloma has also played in the United States for Milwaukee Wave United in the A-League.
In February 2006, Sloma joined Isthmian Premier club Wealdstone before joining Thurrock in the Conference South in April 2006 on dual registration with the "Stones". In 2005, he played for the Great Britain football team at the Maccabiah Games in Israel.
Sloma signed for Dagenham & Redbridge in June 2006. He played two seasons for Dagenham & Redbridge, helping them to achieve Football League status for the first time in their history, scoring their first ever Football League goal. However, he was released at the end of the 2007–08 season alongside Dave Rainford.
In June 2008, Grays Athletic announced Sloma had signed for the Conference National outfit. He scored on his début for the club in the 2–1 home victory over Northwich Victoria in the Conference National, with a 35-yard long range shot.
On 18 November 2008, Sloma scored a goal to put Grays Athletic 1–0 in the lead against Carlisle United in an FA Cup first round clash, only for it to be cancelled due to floodlight failure. The match was replayed on 29 November and Grays lost 2–0.
On 19 January 2009, Sloma was placed on the transfer list by Grays following discussions with the club in which the player stated he would not be staying at the club for the 2009–10 season. His contract at Grays was terminated by mutual consent nine days later. In February 2009, Sloma joined Chelmsford City in the Conference South, teaming up with former Dagenham & Redbridge teammates, Dave Rainford and Chris Moore. On 6 May 2009, Sloma was released from his contract with Chelmsford City.
Sloma joined newly relegated Woking in the Conference South on a one-year contract in June 2009, but was released a year later following an unsuccessful time. He re-signed with former club Wingate & Finchley. For the 2011–12 season he signed for London Lions.Conference National: 2006–07