RALEIGH, N.C.—President Barack Obama will make his campaign-trail debut with Hillary Clinton on Tuesday in North Carolina, launching what is expected to be an aggressive effort by Democrats to regain this swing state in November.

After flipping between the two parties in the last two presidential elections, North Carolina is emerging as a key battleground and a highly trafficked destination for both parties’ presumptive nominees. Republican Donald Trump campaigned in the state earlier this month. Mrs. Clinton was in Raleigh last week, and her campaign announced Wednesday that the president and his former secretary of state would make their inaugural joint appearance in Charlotte next week.

Democrats face a challenge in the state, where the GOP has been on an impressive run in recent years. Republicans gained control of the state legislature in 2010, the governor’s mansion in 2012 and have had both U.S. Senate seats since 2014.

But Mr. Trump’s controversial profile, as well as a backlash to a new bathroom law, have raised Democrats’ hopes. The new law, approved by the GOP-led legislature, requires transgender people to use the bathroom of the sex corresponding to their birth certificate. Republicans said the law was meant to protect public safety, while some businesses, civil-rights groups and the Obama administration called it discriminatory. Legislators are scrambling to roll back parts of the law.

North Carolina is among eight battleground states where the Clinton campaign already is buying ads. The presumptive Democratic nominee has staff on the ground, as well.