San Francisco uses both paper ballots and single transferable voting (in its single-winner, instant runoff voting form). Indeed, I believe all jurisdictions in the United States that use STV also use paper ballots.
In San Francisco, voters vote on paper ballots, and the ballots are electronically scanned. This generates a digital representation of the rankings cast on all ballots, which can be fed into tabulation software. SF actually releases these rankings publicly as a text file for each contest. See here, for example: