A methodology for joining SiC ceramic parts using iridium foil was devised. The connecting layer was formed via a solid-state reaction at 1350 °C or via a transient liquid phase (TLP) at temperatures exceeding 1417 °C. The microstructure of the connecting layer formed via solid-state reaction exhibits temporal changes. The overall thickness of the layer remains approximately constant over time; however, the thickness of the carbon-free central part, composed of Ir and iridium silicides, decreases with time. The thicknesses of the porous carbon-containing sublayers located on either side of the central region demonstrate an increase. The greatest average flexural strength value was found to be 110 ± 6 MPa. The flexural strength values decrease with an increase in the holding time. This behavior can be attributed to the growth of a porous carbon-containing layer. The connecting layer, obtained via a transient liquid phase, is composed of IrSi and C. The layers on either side of the central dense IrSi part contain a number of pores and carbon inclusions. The SiC/SiC joints formed at 1425 °C and 1500 °C exhibit bending strengths of 66 ± 4 and 29 ± 4 MPa, respectively. These findings illustrate the potential of iridium to join monolithic SiC ceramic parts at relatively low temperatures.