When you take a vehicle, change the radio channel to the user tracks player, this station is between WCTR and Radio Off. Now, the audio will be played in the background.
Now, go to Options > Audio config > personal songs options and click on Scan user tracks. First click on S tart > My Documents > Rockstar Games > GTA > User Music.These are the necessary steps that you need to take to do so. To add your own songs and playlists to GTA San Andreas, you will need to Scan user tracks in the Audio config menu. How to add custom background music in GTA San Andreas on PC?