He hailed from the region of Chu 楚 (modern Hubei and Hunan). During the reign of Emperor Wen 漢文帝 (r. 180-157) he was leader of the court gentlemen (zhonglangjiang 中郎將). Yuan Ang suggested to the emperor reducing the size of the territory of the Prince of Huainan 淮南, Liu Zhang 劉長, who had behaved inappropriately, but the Emperor disagreed. Later, when Liu Zhang rebelled and was punished with being sent into exile to Shu 蜀 (modern Sichuan), Yuan Ang against remonstrated against this measure because the death of the Prince on his way to exile brought shame to the Emperor. Yuan Ang was later appointed commandant (duwei 督尉) of Longxi 隴西 (modern Gansu) and became later counsellor to the princes of Qi 齊 and Wu 吳.
Yuan Ang was at odds with Chao Cuo 晁錯, an influential politician at the court, to such an extent that both of them never talked to each other. When Chao Cuo was made Censor-in-chief (yushi dafu 御史大夫) by Emperor Jing 漢景帝 (r. 157-141), Chao accused Yuan Ang to have misappropriated funds of the Prince of Wu 吳, Liu Pi 劉濞. Yuan was demoted to commoner.
When the Seven Princes, among them Liu Pi, rebelled against the emperor, Yuan Ang was again charged to have known about the plans for a revolt. He was nevertheless able to have an audience with Emperor Jing and convinced him that only the death of Chao Cuo, who had wanted to diminish the power of the princes, would appease them. Chao Cuo was indeed executed, and Yuan Ang was appointed chamberlain for ceremonials (taichang 太常) of the Prince of Wu. When the latter offered Yuan Ang to make him general to wage war against the Emperor, Yuan refused and had to flee. When the rebellion of the seven princes was put down, Yuan Ang was appointed counsellor to the prince of Chu, Liu Li 劉禮. Yet he never took over this office and retired into private life.
Later, when Liu Wu 劉武, the Prince of Liang 梁, suggested to Emperor Jing to nominate himself heir apparent, Yuan Ang vehemently contradicted. Full of hatred, Liu Wu sent an assassin to kill Yuan Ang.