Spectroscopic observations of the central 10 pc of M81 were obtained with STIS on board the Hubble Space Telescope during Cycle 7. Measurements of the Hα+[N II] blend reveal a velocity field indicative of a rotating disk of gas. The two-dimensional velocity field has been modeled as a thin disk rotating in a spherical gravitational potential. Minimizing the difference between the model and the observations allows useful constraints to be placed on the mass of the black hole in this mini Seyfert 1 galaxy. The data suggest that the mass of the nuclear black hole in M81 is 7.0+2-1×107 Msolar and that the normal to the disk is inclined at an angle of 14°+/-2° to the line of sight.