He served as Deputy Commander and Chief of Staff of the Joint Combined Special Operations Task Force in Iraq in 2003–2004, receiving the Bronze Star Medal and recommendation for promotion for his service.

In 2000, he was the Republican nominee for the United States House of Representatives in Oregon's 5th congressional district, but lost with 43% of the vote to incumbent Darlene Hooley.

In the 2008 Republican primary, Boquist announced that he was leaving the Oregon House to seek election to the state Senate.

He was unopposed for his party's nomination to represent Oregon Senate District 12 and faced Democrat Kevin Nortness in the general election.

In June 2019, as part of a quorum-busting effort, Boquist and 11 other Republican Senators walked out of a vote on a cap and trade resolution to reduce carbon emissions that cause climate change.

[20] The threat of violence prompted the state Senate's Special Committee on Conduct to hold a hearing on Boquist's comment.

"[16] In July 2019, the four-member committee (which is equally split between Democrats and Republicans), chaired by Floyd Prozanski, opted against temporarily barring Boquist from the Capitol, but unanimously voted to require him to give 12 hours' advance notice to the secretary of the senate before coming to the Capitol, giving officials more time to arrange for additional state troopers to provide security.

[16][21] Boquist sued Courtney, Prozanski, and others over the "12-hour rule" imposed on him, alleging that the discipline violated his First Amendment rights and retaliated against him for constitutionally protected speech.

[23] After a challenge from five Republican Senators the measure was unanimously upheld by the Oregon Supreme Court on February 1, 2024, confirming Boquist's disqualification after the end of his term in January 2025.

[27] Boquist is a practicing Roman Catholic, and at one point attended mass at the same Salem parish as former Democratic Oregon senate president Peter Courtney.