Background: The World Health Organization has set a target of at least 70% of the global population being vaccinated by the middle of 2022. There are only 17 countries that achieved a 70% vaccination rate (VR). This study aims to analyze the effectiveness of public policies to increase the COVID-19 VR. Methods: vaccination figures of all eligible population groups in Hong Kong from 22 February 2021 to 23 January 2022, were extracted for analysis. Weekly acceleration in the VR (AVR) was calculated as a measure of policy effectiveness. A total of 13 identified measures were classified into four policy categories: eligibility, accessibility, incentives, and restrictions. Age-weighted AVR (AWAVR) was compared by age group and policy presence vs. absence using Mann–Whitney U tests. Results: the AWAVR means across age groups ranged from −1.26% to +0.23% (p = 0.12) for eligibility; accessibility ranged from +0.18% to +1.51% (p < 0.0001); incentives ranged from +0.11% to +0.68% (p < 0.0001); and restrictions ranged from +0.02% to +1.25% (p < 0.0001). Conclusions: policies targeting accessibility, incentives, and restrictions are effective at increasing the VR. These results may serve as a policy reference.