Using a data sample of e⁺e^- collisions corresponding to an integrated luminosity of 7.93 fb^-1 collected with the BESIII detector at the center-of-mass energy 3.773 GeV, we perform the first amplitude analysis of the decay D⁺ → K_S⁰K_S⁰π⁺. The absolute branching fraction of D⁺ → K_S⁰K^*π⁺ is measured to be (2.97 ± 0.09_stat ± 0.05_syst) x 10^-3. The dominant intermediate process is D⁺ → K_S⁰K^*(892)⁺, whose branching fraction is determined to be (8.72 ± 0.28_stat ± 0.15_syst) x 10^-3, including all the K*(892)⁺ decays.