We present the first measurements of femtoscopic correlations between the K_S ⁰ and K^± particles in pp collisions at s=7 TeV measured by the ALICE experiment. The observed femtoscopic correlations are consistent with final-state interactions proceeding solely via the a₀(980) resonance. The extracted kaon source radius and correlation strength parameters for K_S ⁰K⁻ are found to be equal within the experimental uncertainties to those for K_S ⁰K⁺. Results of the present study are compared with those from identical-kaon femtoscopic studies also performed with pp collisions at s=7 TeV by ALICE and with a K_S ⁰K^± measurement in Pb–Pb collisions at s_NN=2.76 TeV. Combined with the Pb–Pb results, our pp analysis is found to be compatible with the interpretation of the a₀(980) having a tetraquark structure instead of that of a diquark.