Sen. Roscoe Reynolds' bill applies to the job-training program required to receive welfare. It passed 32-7 Monday.
The bill would require those who apply for, or already receive benefits, to answer questions regarding drug use.
If screeners have reasonable cause to believe the person is using drugs, they can require a drug test.
Individuals who fail a test or refuse to take one would lose their benefits for one year unless they participate in a drug treatment program.
Similar efforts have been unsuccessful in the past because it is estimated to cost more than $1 million for the program.
The bill goes to the House of Delegates.