We present simultaneous NuSTAR and Swift observations of the black hole transient IGR J17091-3642 during its 2016 outburst. By jointly fitting six NuSTAR and four Swift spectra, we found that during this outburst the source evolves from the hard to the hard/soft intermediate and back to the hard state, similar to the 2011 outburst. Unlike in the previous outburst, in this case we observed both a broad emission and an moderately broad absorption line in our observations. Our fits favour an accretion disc with an inclination angle of $sim$$45deg$ with respect to the line of sight and a high iron abundance of $3.5pm0.3$ in units of the solar abundance. We also observed heartbeat variability in one NuSTAR observation. We fitted the phase-resolved spectra of this observation and found that the reflected emission varies independently from the direct emission, whereas in the fits to the average spectra these two quantities are strongly correlated. Assuming that in IGR J17091-3642 the inner radius of the disc both in the average and the phase-resolved spectra is located at the radius of the innermost stable circular orbit, with 90% confidence the spin parameter of the black hole in this system is $-0.13leq a_{*}leq0.27$.