We present the wavelength calibration for the lenslet-based Integral Field Spectrograph (IFS) that serves as the science instrument for the Gemini Planet Imager (GPI). The GPI IFS features a 2.7" x 2.7" field of view and a 190 x 190 lenslet array (14.3 mas/lenslet) operating in Y, J, H, and K bands with spectral resolving power ranging from R similar to 35 to 78. Due to variations across the field of view, a unique wavelength solution is determined for each lenslet characterized by a two-dimensional position, the spectral dispersion, and the rotation of the spectrum with respect to the detector axes. The four free parameters are fit using a constrained Levenberg-Marquardt least-squares minimization algorithm, which compares an individual lenslet's arc lamp spectrum to a simulated arc lamp spectrum. This method enables measurement of spectral positions to better than 1/10th of a pixel on the GPI IFS detector using Gemini's facility calibration lamp unit GCAL, improving spectral extraction accuracy compared to earlier approaches. Using such wavelength calibrations we have measured how internal flexure of the spectrograph with changing zenith angle shifts spectra on the detector. We describe the methods used to compensate for these shifts when assembling datacubes from on-sky observations using GPI.