He attended academies in Salem and White Creek, and then taught school while studying law with Samuel Beardsley and William H. Maynard in Utica and Lauren Ford in Herkimer.

Jenkins was the attorney for the Oneida Indians from 1838 to 1845 as they negotiated with the state of New York to resolve land claims and create reservations.

During his time in Congress, Jenkins was identified as a prominent opponent of slavery, including support for the Wilmot Proviso and opposition to the Kansas–Nebraska Act.

In 1857 he was the unsuccessful Republican nominee for a seat on the New York Court of Appeals, losing to Hiram Denio.

In 1858 he was a candidate for the Republican nomination for Governor of New York, and lost to Edwin D. Morgan, who went on to win the general election.

Jenkins accumulated a large collection of books and papers, including legal and historical works, speeches, and government publications.