We report on results of multi-epoch VLBI observations of H$_2$O masers associated with a low-mass young stellar object, IRAS 16293$-$2422 in $\rho$ Oph East, and a fringe-phase and position reference source, ICRF J162546.8$-$252738, using the VLBI Exploration of Radio Astrometry (VERA) for high-precision astrometry. We obtained an annual parallax of a maser feature to be $\pi=$ 5.6$^{+1.5}_{-0.5}$ mas, corresponding to a distance of $D=178^{+18}_{-37}$ pc. We also found 10 relative proper motions of maser features with respect to the maser feature mentioned above. The motion of the accompanying young stellar object (YSO) has already been found in thermal continuum emission previously observed with the Very Large Array. The intrinsic motions of masers have been estimated from the relative proper motions after the YSO’s motion is subtracted from, and a systemic secular motion of the position reference feature is added to the proper motions originally measured. The intrinsic maser kinematical structure may trace a bipolar outflow.