Spin-orbit torque magnetic random-access memory (SOT-MRAM) exhibits great potential to be next-generation memory. Annealing is an essential process for SOT magnetic tunnel junctions (SOT-MTJs) thin films. To optimize the SOT-MTJ thin films, studying the different dimensions from micro-size to nano-size is very necessary. Here, we investigate the annealing effect on magneto-electric properties of micro-scaled and nano-scaled SOT-MTJs. The tunnel magnetoresistance (TMR) and critical current density (Jc) increase after annealing attributing to the improved crystallization of CoFeB layers and perpendicular magnetic anisotropy (PMA), respectively. However, the TMR increment of micro-scaled SOT-MTJ is larger than that in nano-scale, due to the reduced defects of micro-scaled SOT-MTJs by annealing. Additionally, the Jc of nano-scaled SOT-MTJ is decuple for that of micro-scaled SOT-MTJ because of the improved PMA and diminished thermal effect. This work assesses the different annealing effect in micro- and nano-sized dimensions and supplies experiment foundation to optimize the performance of SOT-MTJs.