On March 8, 2018, Parker became the third member of the House of Representatives to file for Speaker of the Texas House of Representatives to replace Joe Straus, a moderate Republican, who steps down with the regular legislative session in January 2019. He subsequently won reelection on November 6, 52,893 votes (67.2 percent) to 25,852 (32.8 percent) for his Democratic opponent, Laura Haines. Thereafter, he left the speaker's race. His campaign website describes him as an, "Authentic conservative working for HD63."