Orwig served as managing partner of the Dallas office of SNR Denton and was a member of the Litigation and Disputes Department Leadership from 2009 to 2011.

Orwig joined the global law firm Jones Day in 2012, as a Partner of the Business and Tort Litigation Practice in the Dallas office.

In 2017, Orwig became a founding partner of Winston & Strawn’s Dallas office where he was a member of the firm's litigation department before retiring in January 2024.

Orwig began his career as a judicial law clerk for the Halbert O. Woodward, chief judge of the Northern District of Texas.

Orwig joined the United States Department of Justice as an Assistant U.S. Attorney in the Northern District of Texas in 1989.

He stayed there until 1997, when he left to spend a year in Washington D.C. as a Legal Advisor in the Executive Office for United States Attorneys.