Do you still have rights after the oath?

Yes, after taking the Oath of Allegiance you have all the rights of U.S. citizenship, immediately and fully, including the right to vote in federal elections, the right to a U.S. passport, the right to petition for foreign relatives with citizen-priority visa categories, and protection from deportation. The legal mechanism is set out in section 337(a) of the Immigration and Nationality Act, which provides that a person becomes a U.S. citizen at the moment of the oath.

Naturalized citizens have nearly all the same rights as natural-born citizens; the one constitutional exception is that only a natural-born citizen can be elected President or Vice President under Article II, section 1, clause 5 of the Constitution. Otherwise the rights are identical: voting and running for federal office (other than President and Vice President), state and local office, and party leadership; jury service in federal and state courts; the protections of the Bill of Rights and the Fourteenth Amendment, including freedom of speech, religion, press, assembly, and petition, the right to keep and bear arms, due process, equal protection, and the rights of the accused; the right to a U.S. passport and consular protection abroad; the right to file Form I-130 petitions for spouses, parents, children, and siblings; eligibility for federal benefits limited to citizens, including most full federal employment positions; and protection from deportation (section 237 of the INA generally cannot be used against a U.S. citizen).

The new citizen also assumes the duties of citizenship: obeying federal, state, and local laws, paying taxes, registering for Selective Service if a male aged 18 to 25, and serving on a jury when called.