At the beginning of the COVID-19 pandemic in the US, traffic sharply fell due to social distancing policies in many locations. Correspondingly, many regions observed an increase in traffic volume (traffic recovery) as the pandemic eased in 2022. We examine how vaccination rates influence traffic recovery in Los Angeles County (LAC), controlling for differences in case counts, demographics, and socioeconomic factors across areas with different vaccination rates. We use arterial road sensor data as a proxy for the traffic volume near each ZIP code, alongside their respective demographic and socioeconomic characteristics. We find that a higher vaccination rate is statistically significantly associated with a larger traffic recovery, a finding that remains consistent across all explored models. This implies that a rise in the vaccination rate might enhance the public's perception of protection, leading to a larger traffic recovery. Moreover, we found that variables including population, income, race, work industry, and commuting preferences were correlated with vaccination rates. This highlights potential inequalities based on race, income, and industry sectors in the COVID-19 vaccination and a return to normal traffic flow.