The acoustic scattering properties of an obstacle are completely described by its infinite acoustic T-matrix. The T-matrix is particularly useful when one is interested in analysing changes in sound wave propagation with respect to various changes in orientation or configuration of single or multiple scatterers. This is because the T-matrix is independent of the incoming wave directions and hence can be used to easily simulate the scattered sound waves, without the need to fully set up and solve each reconfigured system. However, in practice one must use the truncated finite dimensional T-matrix, which is usually computed using the null field method. For acoustically large obstacles or highly non-spherical particles the null field method is numerically unstable. In this work we describe an eficient and stable method for computing the truncated T-matrix using a surface integral equation reformulation and a high order acoustic surface scattering algorithm.