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Many 'Tiger King' fans were stunned to find out Joe Exotic doesn't sing his own songs, but there's a real band behind those cat-themed country tunes ... and it hopes the hit Netflix docuseries leads to a record deal.

For those who haven't watched yet ... zoo owner/big cat breeder Joe Exotic flaunts his country music songs and videos on 'Tiger King,' but it turns out he's just lip-syncing and pretending to play the guitar. The real performers are The Clinton Johnson Band.

One-half of the country group, Vince Johnson, tells TMZ ... since the documentary premiered and became a smashing success, lots of journalists and media outlets have reached out to him ... but he'd prefer to get some calls from music labels. So far, no luck.

Vince says that's a shame, because he and the other half of the band, Danny Clinton, recorded 3 albums worth of songs before Danny passed away in October from a heart-related issue.

We're told their tracks are a lot like the ones they did for Joe in 'Tiger King' ... except they're not cat-related.

Vince tells us the band's had some prior success getting their work featured in some small films and TV shows like "Justified," but he believes 'Tiger King' could really be a big break ... and help him become a big cat in the music biz.

As for how The CB Band -- from Vancouver, Washington -- got linked up with the Oklahoma zoo extraordinaire ... Vince tells us they simply responded to one of Joe's ads to make a theme song for Joe's TV show and park, and it evolved from there.

He says how it worked was Exotic would give Vince a theme and some details, he'd write a tune and Danny would sing it. Then they'd email it to Joe.

The band did about 20 songs for Joe, Vince says, and as far as he knows ... Joe has never professionally sung or played an instrument in his life.