The microstructure and properties of non-linear friction stir welded lap joints of the AA6061-T6 aluminum alloy were investigated, with a particular focus on the influence of corner curvature on the formability and mechanical properties of the joints. The research results indicate that for the 6061-T6 aluminum alloy lap joint friction stir welding with a smaller radius (R < 7 mm), there is a more severe accumulation of welding material. When the radius exceeds 7 mm, good macroscopic joint formation can be achieved. Various regions at the joint corners are composed of α-Al and intermetallic precipitations β phases. The microstructure of the heat-affected zone (HAZ) appeared relatively coarse, the weld nugget zone (WNZ) had the finest grain, and partial dissolution of the β phase occurred. The grain size in the middle WNZ at the corner was larger than at the ends, and the grain size on the inner side of the corner was larger than on the outer side. The hardness distribution of the joint exhibited a “W” shape, with the lowest hardness in the inner HAZ. When R ≤ 7, with an increase in R, the shear strength of the friction stir welded joints increased, and then the change became relatively small. The maximum shear strength of the joint was 101.32 ± 6.89 MPa at R = 7, and the fracture mode was primarily a ductile mixed fracture.