He served in the Maryland militia during the American Revolutionary War as private, lieutenant, and later as captain.

In 1800, Wright was elected as a Democratic Republican to the United States Senate on November 19, 1801, for the term commencing March 4, 1801.

He resigned from the Senate on November 12, 1806, having been elected the 12th Governor of Maryland, a position he served in from 1806 to 1809.

After his tenure as governor, Wright served as clerk of Queen Anne's County, Maryland, in 1810, and was elected to the Eleventh and Twelfth Congresses to fill the vacancy caused by the resignation of John Brown.

He is interred in the private burying ground of the DeCourcy family at Cheston-on-Wye in Queen Anne's County.