In this experiment, a Sn35Bi0.3Ag–xIn (x = 0, 0.5, 1.0, 1.5) alloy solder was prepared by electromagnetic induction heating furnace. The effects of In on the thermodynamic properties, wettability, interface microstructure, and soldering performance of Sn35Bi0.3Ag–xIn/Cu solder joints were studied by a synchrotron thermal analyzer (DSC), contact-angle measuring instrument, scanning electron microscope (SEM), energy dispersive spectrometer (EDS), and universal tensile testing machine. The research showed that adding a small amount of In reduced the solid–liquid temperature and improved the wettability of the alloy solder. At the interface of SnBiAg–xIn/Cu joint, it was found that In atoms replaced part of Sn atoms, forming the Cu6 (Sn, In)5 phase and scallop-like Cu3 (Sn, In) phase. When adding 0.5% and 1.0% In elements, it was found that the Bi phase appeared on the solder side of the interface layer, which hindered the growth of the intermetallic compound (IMC) and reduced the thickness of the IMC layer. Among them, the thickness of the IMC layer of the SnBiAg–1.0In/Cu joint was the smallest, and the shear strength was the highest, which was 55.1 MPa. In addition, the fracture morphology of the solder joint was observed, and it was found that the fracture mode was brittle fracture, and the SnBiAg–xIn/Cu solder joint fractured from the IMC and solder side.