If you want to become a rapper in Bitlife, you can't as there isn't a dedicated job for it. However, there is an option to record a rap album, but you must first become a solo artist to do this.
If you want to become a solo artist, you will need to create your character in Bitlife and age to the point where you are six years old.
After this, you will then need to go to the body and mind tab and find the instruments option. From this tab, you will be able to start taking music lessons - it doesn't matter the instrument, just pick whatever suits you the best.
Along with an instrument, you will also need to take voice lessons before you can become a solo artist. That said, once you picked both , make sure to practice every year as you age until you finish high school.
Related: How to Join a band in Bitlife
At this point, you will turn eighteen and should have the talents of both an instrument and a singer engrained in you. If this is the case, the next step would be to try applying to record labels to record rap albums when they pop under the list of jobs.
However, be ready to get rejected a lot as it is a high possibility, and if that happens the best solution would be to practice and hone your skills. You can also try closing the app and restarting the game if you get rejected by a record label.