Born in Roswell, New Mexico, Burciaga received a Bachelor of Science degree from the United States Military Academy in 1952 and was a United States Air Force pilot from 1952 to 1959.

He was also a lecturer at the University of New Mexico School of Law from 1970 to 1971, and was a special prosecutor for the First Judicial District in Santa Fe in 1975.

He was confirmed by the United States Senate on October 31, 1979, and received his commission on November 2, 1979.

[1] Burciaga served until his death on March 5, 1995, at the Presbyterian Hospital in Albuquerque of an aortic aneurysm.

[2] Burciaga ruled against the National Collegiate Athletic Association in a case that allowed schools to contract television rights for their football programs thus leading to the many games seen now.