We have measured an annual parallax of the Mira variable R~Ursae~Majoris (R~UMa) with the VLBI exploration for Radio Astronomy (VERA). From the monitoring VLBI observations spanning about two years, we detected H$_2$O maser spots in the LSR velocities ranges from 37 to 42 km,s$^{-1}$. We derived an annual parallax of 1.97$pm$0.05,mas, and it gives a corresponding distance of 508$pm$13,pc. The VLBI maps revealed 72 maser spots distributed in $sim$110 au area around an expected stellar position. Circumstellar kinematics of the maser spots were also revealed by subtracting a systemic motion in the Hipparcos catalog from proper motions of each maser spots derived from our VLBI observations. Infrared photometry is also conducted to measure a $K$ band apparent magnitude, and we obtained a mean magnitude of $m_K$ = 1.19$pm$0.02,mag. Using the trigonometric distance, the $m_K$ is converted to a $K$ band absolute magnitude of $M_K = -$7.34$pm$0.06,mag. This result gives a much more accurate absolute magnitude of R~UMa than previously provided. We solved a zero-point of $M_K - log P$ relation for the Galactic Mira variables and obtained a relation of $M_K = -$3.52 $log P$ + (1.09 $pm$ 0.14). Other long period variables including red supergiants, whose distances were determined from astrometric VLBI, were also compiled to explore the different sequences of $M_K - log P$ relation.
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