From Kha-Potshangbam, Manipur, Singh joined Pune FC academy in 2011 and was part of the U-19 side which won the Hero Elite League twice.
He went on to represent Maharashtra in the 2013 Santosh Trophy and was soon called up to the Pune FC senior team which was competing in the I-League. In his very first season, he featured in 18 matches which came in the I-League as well as in the AFC Cup competition.
After Pune FC withdrew from the I-League in October of 2015, Ranjan joined Bengaluru FC on loan and ended up making an appearance in the 2016 AFC Cup Final which Bengaluru FC eventually lost. A brief stint at Northeast United in the ISL followed before the defender rejoined Bengaluru FC for the 2016-17 I-League.
After a season at Benglauru, Salam Ranjan Singh moved to East Bengal on a free transfer in June 2017. He featured heavily in his first season at the Kolkata club in the I-League and was also called up to the national team by Stephen Constantine. The 23-year old has been capped 11 times for the national side.