The 33-year-old, who suffers from cerebral palsy and profound deafness, won a bronze in the Paralympics Grade IA individual championship dressage test with a score of 73.650.
She finished behind Britain's Sophie Christiansen (82.750) and Ireland's Helen Kearney (76.700).
Tan, who is based in the United Kingdom, won two bronzes at the 2008 Beijing Paralympic Games and will be awarded S$50,000 for her achievement in London.
A delighted Tan said, "I had a smooth ride and it all went well. I'm happy that I got the medal as the competition standard is higher and harder this time.
"I'm really happy and it hasn't quite sunk in yet. I have worked hard and I am grateful to the team and all the members for all the help and support provided."
Fellow Singaporean Gemma Foo finished 13th place out of 14 with a score of 65.050.