Before moving to Scotland, Andrews played with Carib F.C. of Trinidad.
Tall, strong and very good in the air as he has proven to be with a few goals over the years, Raith Rovers sold Andrews for around £50,000 in a multi-player deal. Andrews signed for Livingston on 28 September 2000. Andrews was voted Raith Rovers’ “Player of the Day” in the 1999–00 season and, also Livingston’s “Player of the Year” for the 2003–04 season. On 14 March 2004, Andrews picked up his first major medal when Livingston won the 2003-04 Scottish League Cup by beating Hibernian 2–0 with goals by Derek Lilley and Jamie McAllister.
Andrews signed a two-year deal with Rangers in May 2004 and at the end of his first season with Rangers he scooped the Rangers Players’ Player of the Year award, the club also won the Scottish Premier League title on the last day of the season. He was released by Rangers at the end of the 2005–06 season and was a free agent for a short while, before being re-signed by his former club Raith Rovers on 4 October 2006.
In May 2008, Andrews left Raith by mutual consent. He appeared for them as a trialist a little less than a year later, playing for the full 90 minutes in a 1–0 win over East Fife. Andrews stated that he wishes to remain with Rovers for the rest of the season and signed up yet again to Raith Rovers on 11 March 2009. In July 2009, Andrews signed for SPL club Hamilton Academical.
On 7 December 2009, Dumfries club Queen of the South announced Andrews had signed on a one-month loan as cover for the suspended David Lilley and Stephen McKenna. Manager Gordon Chisholm gave Andrews his Queens debut on 12 December in the 2–1 win away to Morton. With bad weather causing a series of fixture postponements at Palmerston Park, Andrews played only one other game for Queens during the loan period, in the 2–2 draw away at Partick Thistle. However Andrews returned to QoS by signing a six-month deal on 29 January 2010. Andrews was released by Queens at the end of the 2009–10 season.
He joined Wrexham in August 2010 on a short term contract for the 2010–11 season in the Conference Premier. At the end of 2011, he left Wrexham and joined Scottish Junior Football Association, West Region club Kirkintilloch Rob Roy.
At the start of 2013, he joined Albion Rovers in the Second Division. In July 2013, it was confirmed that he had signed for Forfar Athletic.
On 10 August 2014, Andrews made his debut for League Two side Elgin City. Andrews set up Craig Gunn to score the only goal of the game, as Elgin beat East Fife 1–0. After three games as a trialist, including two man of the match performances and one goal against Annan Athletic, Andrews signed a one-year deal with Elgin. He is quoted as saying “It’s a very, very nice club with great supporters, and the team plays very attractive football.” He scored his second goal for Elgin in a 5-4 defeat to Bo’ness United F.C. in the Scottish Cup.
In January 2015 he joined Montrose, and scored his first goal for the club in a 3-3 draw with Berwick Rangers. On 16 May 2015, Andrews scored as Montrose came from behind to defeat Highland Football League champions Brora Rangers in a play-off to maintain their status in the SPFL. In September 2015, at the age of 39, Andrews signed for Clyde, playing in Scottish League Two. He scored on his debut against former club Elgin City. After playing in just 13 League matches, Marvin was released by the club at the end of the 2015–16 season.