Robinson was born in Hardwick, Massachusetts. He moved with his family to Bennington, Vermont at the age of five. Robinson did not enter politics until he was about thirty years old, when his brother Moses Robinson became a successful politician.
Jonathan Robinson was elected to the Vermont House of Representatives in 1789. A few years later he decided to study law and passed the bar exam in 1795. He was admitted to the bar in 1796. Immediately after, he became a judge of the Vermont probate court and the town clerk of Bennington. He was a probate judge until 1798.
In 1801, Robinson was appointed to be the chief justice of the Vermont Supreme Court, and soon left his positions as state representative and town clerk. He remained the chief justice until 1807, when he gained a position in the United States Senate from Vermont, filling the unexpired term of Israel Smith, who had resigned. Robinson was a member of the Democratic-Republican Party. He was elected to a full term in the Senate in 1809 and remained a senator until 1815, when he retired after the end of his term. Robinson then served again as a probate judge from 1815 until his death four years later, and served for one more year in the Vermont House of Representatives in 1818.