WASHINGTON—The U.S. Department of Homeland Security is working on a plan to scrutinize social media posts as part of its visa application process before certain people are allowed entry into the nation, a person familiar with the matter said.

The move is part of a new focus on the use of social networking sites following the shooting rampage in San Bernardino, Calif., the person added.

Currently, DHS only looks at these postings intermittently and as part of three pilot programs that began in earnest earlier this year. It’s unclear how quickly a new process could be implemented, and other details couldn’t be learned.

Investigators currently are looking for clues in Facebook posts, computer records, and elsewhere that might have hinted at the intentions of the husband-and-wife team Syed Rizwan Farook and Tashfeen Malik, accused of killing 14 people at a holiday gathering on Dec. 2 before dying in a shootout with police.

Ms. Malik lived most of her life in Pakistan and Saudi Arabia, but moved to the U.S. in 2014 on a K-1 visa—the type given to fiancées of Americans. The day of the shooting, Ms. Malik pledged allegiance to the leader of the Islamic State terror group on a Facebook account registered to a pseudonym, and counterterrorism officials are looking to see whether she made similar social media posts in the past.