Current is captain of Investigations and Administration. He will oversee detectives, administration, civilian employees, evidence and property.
The promotion was announced Thursday.
The other sheriff's office captain, Shane Utley, oversees day and night patrol officers.
The only positions ranked above captains at the sheriff's office are the sheriff and undersheriff.
Current, 35, has been in law enforcement since 2000. He has worked as a patrol officer, detective, instructor and was a member of the SWAT team.
He also worked two years as an undercover agent for the Region II Narcotics Task Force.
"It's not like most people think. You're not out with a biker gang living in their houses," he said. "It's one of the most defining moments of your career. You learn a lot about life, and the town and you work with local and state" agencies.
He said undercover work included finding contacts throughout town and making drug or gun purchases and working up to build bigger and bigger cases against suspects.
"Brice is ideally qualified for this position because of the various positions he has held within law enforcement," Sheriff Ken Christesen said in a statement. "He is excellent in handling any problem that he encounters and exemplifies the type of leadership that is essential to our office."