This paper uses the multi-epoch astrometry from the Wide-field Infrared Survey Explorer (WISE) to demonstrate a method to measure proper motions and trigonometric parallaxes with precisions of ~4mas/yr and ~7mas, respectively, for low-mass stars and brown dwarfs. This method relies on WISE single exposures (Level 1b frames) and a Markov Chain Monte Carlo method. The limitations of Gaia in observing very low-mass stars and brown dwarfs are discussed, and it is shown that WISE will be able to measure astrometry past the 95% completeness limit and magnitude limit of Gaia (L, T, and Y dwarfs fainter than G~=19 and G=21, respectively). This method is applied to WISE data of 20 nearby (<=17pc) dwarfs with spectral types between M6-Y2 and previously measured trigonometric parallaxes. Also provided are WISE astrometric measurements for 23 additional low-mass dwarfs with spectral types between M6-T7 and estimated photometric distances <17pc. Only nine of these objects contain parallaxes within Gaia Data Release 2.