Joseph P. Robinson was born around 1840 in Maryland to John and Hannah Robinson. His father was a minister. By 1855, the family was living in West Roxbury, Massachusetts. By 1860, they were living in Boston, Massachusetts, and Robinson was working as a clerk.
In September 1862, he received a commission as a 2nd lieutenant in the 32nd Massachusetts Infantry. In early 1863, he served on detached duty as a quartermaster in Washington, D.C. He was promoted to 1st lieutenant in March 1863. He mustered out on July 14, 1865, and he died sometime after the war.