The Renner-Teller effect in C2H2+(X-2 Pi(u)) has been studied by using zero kinetic energy (ZEKE) photoelectron spectroscopy and coherent extreme ultraviolet (XUV) radiation. The rotationally resolved vibronic spectra have been recorded for energies up to 2000 cm(-1) above the ground vibrational state. The CtC symmetric stretching (nu(2)), the CCH trans bending (nu(4)), and the CCH cis bending (nu(5)) vibrational excitations have been observed. The assigned vibronic bands are 4(1)(1)(kappa(2)Sigma(+)(u))(hot band), 4(0)(1)(mu/kappa(2)Sigma(-/+)(u)), 5(0)(1)(mu/kappa(2)Sigma(+/-)(g)), and 4(0)(2)(mu(2)Pi(u)), 4(0)(2)(kappa(2)Pi(u)), 4(0)(1)5(0)(1)(mu(2)Pi(g)), 0(0)(0)(X-2 Pi(u)), and 2(0)(1)(X-2 Pi(u)). The Renner-Teller parameters, the harmonic frequencies, the spin-orbit coupling constants, and the rotational constants for the corresponding vibronic bands have been determined by fitting the spectra with energy eigenvalues from the Hamiltonian that considers simultaneously Renner-Teller coupling, vibrational energies, rotational energies, and spin-orbit coupling interaction.