Robinson was born in Dublin. He was educated at Belfast Academy then continued his studies at Trinity College, Dublin, and obtained a fellowship in 1814; for some years he was deputy professor of natural philosophy, until in 1821 he obtained the college living of Enniskillen. In 1823 he was appointed astronomer of the Armagh observatory, with which he (from 1824) combined the living of Carrickmacross, but he always resided at the observatory, engaged in researches connected with astronomy and physics, until his death in 1882.
Robinson published a number of papers in scientific journals, and the Armagh catalogue of stars places of thousands of stars observed from 1828 to 1854 at the Armagh Observatory, Dublin, (1859). He is best known as the inventor (1846) of the cup-anemometer for registering the velocity of the wind.