In 2021, Parker proposed a bill to allow people to have loaded guns in their vehicles on school grounds. The legislation passed the House on a 31–28 party-line vote.[5]
Parker introduced a bill to give Arizona Attorney GeneralMark Brnovich the power to sue the Arizona Board of Regents over tuition at Arizona public universities. Brnovich previously sued the Board in 2017; the suit was unsuccessful, as the Arizona Supreme Court ruled in November 2020 that Brnovich lacked the power to maintain the suit against the board. Parker's bill failed after a single Republican, Michelle Udall, joined all the Democrats in voting no.[6]
Parker introduced a bill in 2021 to give the Legislature more power over the Arizona Corporation Commission through forcing the state attorney general to investigate. The bill was introduced over a dispute over the role of the Commission versus the Legislature over powers to regulate utilities and set energy policy. Democratic members of the Commission favored renewable portfolio standard, while Republican members of the Commission and Republican Governor Doug Ducey took steps to block the Commission from adopting such standards. Democratic Commissioner Anna Tovar suggested that the bill violated the Arizona Constitution, and that Parker had introduced it at the behest of her former boss, Commissioner Olson, or Ducey.[1]
Parker is anti-abortion. In 2024, she voted against a legislative proposal to repeal a 1864 law that imposed a near-total ban on abortion in Arizona.[7]