Twisted ion-acoustic excitations and the existence of kinetic instability are investigated in this study, accounting for finite orbital angular momentum states. For this purpose, a quasi-neutral electron-ion plasma is considered, which permeates through another (target) plasma. The Vlasov-Poisson model is used to obtain explicit expressions for wave dispersion and kinetic instability, including the contributions from the orbital angular momentum. It is shown that the existence of instability is a result of the exceeding electron speed as compared to the ion-acoustic speed, with a strong contribution of twist in the wave. Furthermore, it is found that a planner ion-acoustic wave propagates as a slow wave in comparison with the non-planar (twisted) wave. The results are analysed numerically for typical plasmas found in space and astrophysical environments.