Technically you can license parts of a soundtrack through your country‘s performance rights organisation. For Germany it’s GEMA, for the US it’s BMI or ASCAP (AFAIK). You’d have to pay royalties for the use of the track.
However, I recommend commissioning a composer to create unique music for your game instead if you want your game to stand out! I’m sure there are plenty of promising young talents who’d happily take the job and tailor the music to the situation you want to portray. Do pay them fairly though!
Either that or you can look for royalty-free music online. You pay one set fee and are allowed to use it as you wish. Or use Creative Commons music, which you can find on sites like Jamendo. Depending on the type of CC license, some tracks can be used for free, as long as you credit the artist.