Understanding parental decision-making about vaccinating their children for COVID-19 is essential to promoting uptake. We conducted an online survey between April 23-May 3, 2021, among a national sample of U.S. adults to assess parental willingness to vaccinate their child(ren). We also examined associations between parental intentions to VACCINATE their children for COVID-19 and conspiracy theory beliefs, trusted information sources, trust in public authorities, and perceptions regarding the responsibility to be vaccinated. Of 257 parents of children under 18 years that responded, 48.2% reported that they would vaccinate their children, 25.7% were unsure, and 26.1% said they would not vaccinate. After adjusting for covariates, each one-point increase in the Vaccine Conspiracy Beliefs Scale was associated with 25% lower odds of parents intending to vaccinate their children compared to those who did not intend to (adjusted odds ratio (AOR) = 0.75, 95% confidence interval (CI): 0.64-0.88). Parents that perceived an individual and societal responsibility to be vaccinated were more likely to report that they intended to vaccinate their children compared to those that did not intend to vaccinate their children (AOR = 5.65, 95% CI: 2.37-13.44). Findings suggest that interventions should focus on combatting conspiracy beliefs, promoting accurate and trusted information sources, and creating social norms emphasizing shared responsibility for vaccination.