A cross-sectional survey design was used to assess Arkansas parents’/guardians’ intentions to vaccinate their child against COVID-19. Parents/guardians whose oldest child was age 0–11 years (n = 171) or 12–17 years (n = 198) were recruited between 12 July and 30 July 2021 through random digit dialing. Among parents/guardians with an age-eligible child, age 12–17, 19% reported their child had been vaccinated, and 34% reported they would have their child vaccinated right away. Among parents/guardians with a child aged 0–11, 33% of parents/guardians reported they would have their child vaccinated right away. Twenty-eight percent (28%) of parents/guardians whose oldest child was 12–17 and 26% of parents/guardians whose oldest child was 0–11 reported they would only have their child vaccinated if their school required it; otherwise, they would definitely not vaccinate them. For both groups, parents’/guardians’ education, COVID-19 vaccination status, and COVID-19 vaccine hesitancy were significantly associated with intentions to vaccinate their child. More than a third of parents/guardians whose child was eligible for vaccination at the time of the survey reported they intended to have them vaccinated right away; however, they had not vaccinated their child more than two months after approval. This finding raises questions about the remaining barriers constraining some parents/guardians from vaccinating their child.