The level density and γ-ray strength function (γSF) of Pu243 have been measured in the quasicontinuum using the Oslo method. Excited states in Pu243 were populated using the Pu242(d,p) reaction. The level density closely follows the constant-temperature level density formula for excitation energies above the pairing gap. The γSF displays a double-humped resonance at low energy as also seen in previous investigations of actinide isotopes. The structure is interpreted as the scissors resonance and has a centroid of ωSR=2.42(5) MeV and a total strength of BSR=10.1(15)μN2, which is in excellent agreement with sum-rule estimates. The measured level density and γSF were used to calculate the Pu242(n,γ) cross section in a neutron energy range for which there were previously no measured data.