The far-field acoustic radiation due to the interaction of upstream, unsteady vortical disturbances with an airfoil in subsonic, compressible flow is calculated using potential theory. A Kirchhoff surface is placed in the near field surrounding the airfoil and the pressure on this surface is calculated from the unsteady flow field, obtained using a second-order finite-difference code. The governing equation is reduced to the Helmholtz equation in the frequency domain and the solution is written in terms of an integral over the Kirchhoff surface involving the free-space Green's function and an unknown single-layer density function. The single-layer density is then determined from the boundary condition on the Kirchhoff surface. This method is presented as an alternative to classical Kirchhoff methods. It has the advantage of being able to accommodate arbitrarily shaped Kirchhoff surfaces and is also readily extendable to three-dimensional problems. Numerical results are presented for thin, symmetric, and loaded airfoils. Thin-airfoil results are compared to the analytical solution, and thick-airfoil results are checked for numerical convergence and compared to results obtained from a time-domain Euler solver.