In this paper, using the Non-Equilibrium Green Function (NEGF) formalism, we have calculated the electron transport through a silicon nanowire with a rough interface. The nanowire was orientated in the [100] direction. Two different wire diameters, D1 = 2.18 nm and D2 = 3.21 nm, have been used to analyse the effect of the cross section in the transmission coefficients. We used a full-band description of the electron state by using a tight binding formalism to describe the electron Hamiltonian. The calculation makes full use of the recursive algorithm to calculate the transmission. We compare several nanowires that differ in the microscopic realization of interface roughness. The energy shift between the onset of the transmission of the rough and the pristine nanowire are 200 meV and 50 meV for D1 and D2 respectively. Furthermore, the transmissions of some nanowires show resonances due to a resonant cavity created by the interface surface. This is particularly relevant as effective-mass-approximation NEGF simulations of similar nanowire transistors show the same resonances. These resonances play a role in increasing the off-current of nanowire transistors.