We report on the deflection of laser pulses and accelerated electrons in a laser-plasma accelerator (LPA) by the effects of laser pulse front tilt and transverse density gradients. Asymmetry in the plasma index of refraction leads to laser steering, which can be due to a density gradient or spatiotemporal coupling of the laser pulse. The transverse forces from the skewed plasma wave can also lead to electron deflection relative to the laser. Quantitative models are proposed for both the laser and electron steering, which are confirmed by particle-in-cell simulations. Experiments with the BELLA Petawatt Laser are presented which show controllable 0.1-1 mrad laser and electron beam deflection from laser pulse front tilt. This has potential applications for electron beam pointing control, which is of paramount importance for LPA applications.