I have seen that the original estimate to pass by Mars was about 6 months, but the current trajectory overshot Mars by quite a bit. How long until Starman and the Roadster return to complete their first orbit of the sun?
After seeing the other @MarkAdler comment, I looked and sure enough a projected orbit is in Horizons based on the last, best data from the FH 2nd stage's navigation information.
I get 558 days and I show the math, or at least the Python that extracts the data from Horizons.
Update: JPL Horizons is now providing data based on a refined calculation:
TRAJECTORY: This trajectory is based on JPL solution #8, a fit to 330 ground-based optical astrometric measurements spanning 2018 Feb 8.2 to 18.3
Based on this, the period is now given as 557.1 days, rather than the original 558 days.
This answer will take you to a detailed list of the (now more than) 330 individual astrometric observations of Roadster.
2.404 years, by doing the math.
Of course, that assumes that the orbital parameters used were correct. According to many internet sleuths, the C3 value given doesn't match the orbital parameters. The correct value is more likely to be around 1.6 years, according to this tweet.