We studied electron carrier doping into the ternary wurtzite β-AgGaO2 by impurity doping. Ti-doped β-NaGaO2, i.e., β-Na(Ga1-xTix)O2, was prepared by a conventional high-temperature solid-state reaction; then, we performed ion-exchange of Na+ ions with Ag+ ions into the Ti-doped β-NaGaO2 in a molten nitrate salt to produce Ti-doped β-AgGaO2: β-Ag(Ga1-xTix)O2. A single ternary wurtzite phase was obtained at compositions of 0≤x≤0.05. Ti-doped β-AgGaO2 showed an electrical conductivity at room temperature that was one to three orders of magnitude higher than that of undoped β-AgGaO2. The Ti-doped β-AgGaO2 samples showed an electron carrier density in the range of 1018-1019 cm-3, based on the free-carrier absorption shown in their optical absorption spectra. These results show that carrier injection by impurity doping into metastable β-CuMIIIO2 and β-AgMIIIO2 is possible by using an impurity-doped β-NaGaO2 precursor. This result encourages the development of optoelectronic devices based on the narrow-band-gap oxide semiconductors of β-CuMIIIO2 and β-AgMIIIO2.