The influence of the stoichiometry of amorphous zinc tin oxide (a-ZTO) thin films used as the semiconducting channel in thin film transistors (TFTs) is investigated. A-ZTO has been deposited using remote-plasma reactive sputtering from zinc:tin metal alloy targets with 10%, 33%, and 50% Sn at. %. Optimisations of thin films are performed by varying the oxygen flow, which is used as the reactive gas. The structural, optical, and electrical properties are investigated for the optimised films, which, after a post-deposition annealing at 500 °C in air, are also incorporated as the channel layer in TFTs. The optical band gap of a-ZTO films slightly increases from 3.5 to 3.8 eV with increasing tin content, with an average transmission ∼90% in the visible range. The surface roughness and crystallographic properties of the films are very similar before and after annealing. An a-ZTO TFT produced from the 10% Sn target shows a threshold voltage of 8 V, a switching ratio of 10$8$, a sub-threshold slope of 0.55 V dec$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, and a field effect mobility of 15 cm$2$ V$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, which is a sharp increase from 0.8 cm$2$ V$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ obtained in a reference ZnO TFT. For TFTs produced from the 33% Sn target, the mobility is further increased to 21 cm$2$ V$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, but the sub-threshold slope is slightly deteriorated to 0.65 V dec$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. For TFTs produced from the 50% Sn target, the devices can no longer be switched off (i.e., there is no channel depletion). The effect of tin content on the TFT electrical performance is explained in the light of preferential sputtering encountered in reactive sputtering, which resulted in films sputtered from 10% and 33% Sn to be stoichiometrically close to the common Zn$2$SnO$4$ and ZnSnO$3$ phases.