Yes, you can wear a hijab in the Vatican.
The Vatican is a religious institution, and while hats are generally not allowed inside for secular reasons, exceptions are made for religious head coverings. A hijab, being a religious headscarf worn by Muslim women, is permissible. This aligns with the Vatican's general respect for religious expression and the understanding that head coverings are sometimes integral to certain faiths.
Therefore, wearing a hijab within the Vatican, including St. Peter's Basilica and other religious sites, is acceptable. Just be mindful and respectful of the religious environment.