Born in Reno, Nevada, Norcross received an Artium Baccalaureus degree from the University of Nevada, Reno in 1891 and a Bachelor of Laws from Georgetown Law in 1894.

He was a district attorney of Washoe County, Nevada from 1895 to 1897.

[1] On April 2, 1928, Norcross was nominated by President Calvin Coolidge to a seat on the United States District Court for the District of Nevada vacated by Judge Edward Silsby Farrington.

Norcross was confirmed by the United States Senate on April 17, 1928, and received his commission the same day.

He assumed senior status on April 30, 1945 serving in that capacity until his death on November 4, 1952, in San Francisco, California.