He told the state party convention in Los Angeles on Saturday that those issues shouldn't be the purview of Democrats. He says when the Republican Party "looks like the rest of America" they'll win again.
Paul has been pushing a libertarian approach to expand the GOP's base this year ahead of a possible 2016 presidential bid.
Most of his address to about 400 people covered familiar turf for Paul, such as connecting with millennial voters on civil liberties issues.
He did not touch on his vote this week against President Barack Obama's legislation to authorize military involvement in Syria.