As a faithful Catholic, can I obtain a religious exemption from accepting COVID vaccination?

Excellent question! To some extent, it appears to depend on where you live. There is significant disagreement even among Bishops on this topic. In particular, the Archdiocese of New York has said that their diocesan priests are not to endorse such exemptions, while the Bishops of Colorado have gone so far as to provide a template for requesting just such an exemption.