In 1824 he was admitted to practice in Superior Court at Albany, New York.
Peck served from 1839 to 1841 as chancellor of the Middle Division Chancery Court.
Peck was an opponent of secession but did not actively aid the cause of the Union during the Civil War.
He was a candidate for representative to the Alabama Constitutional Convention of 1865 but was defeated.
Later that year, Peck, a member of the Republican Party, was chosen as chief justice of the Alabama Supreme Court, where he served until retiring in 1874.