Control of electron transport through molecular devices is a fundamental step toward design of functional molecular electronics. In this respect, the application of the field-effect transistor principle to molecular junctions appears to be a desirable strategy. Here we study the possibility of mechanically controlling the molecular orbital alignment in self-assembled monolayers via the electrostatic fields originating from dipoles at the metal-molecule interfaces. More specifically, we analyze first-principles simulations of prototype alkanedithiolate and alkanediamine monolayer junctions between Au(111) electrodes as a function of inclination of the molecules in the film. We find that the molecular orbital alignment and hence the low-bias conductance of the junctions, sensitively depends on the interface dipole. The dipole change with molecular tilt is rationalized in terms of two electrostatic effects: (i) the reorientation of a dipole associated with the anchoring group and (ii) a dipole modification arising from charge redistribution due to the metal-molecule bond. The first effect, dominating for the thiolates, is the desired way to gate the junctions by tuning of the molecular tilt. However, the second effect, equally important for the amines, may hamper the mechanical control of the level alignment because it depends on other geometric details than the tilt angle. Our results thus suggest that mechanical gating by tilt is achievable with molecules and anchoring groups with strong intrinsic dipole moments and well-defined binding geometry rather than with interface dipoles associated with weak and flexible metal-molecule bonds.