We investigate the influence of a tilted laser-pulse-intensity front on laser-wakefield acceleration. Such asymmetric light pulses may be exploited to obtain control over the electron-bunch-pointing direction and in our case allowed for reproducible electron-beam steering in an all-optical way within an 8 mrad opening window with respect to the initial laser axis. We also discovered evidence of collective electron-betatron oscillations due to off-axis electron injection into the wakefield induced by a pulse-front tilt. These findings are supported by 3D particle-in-cell simulations.