No

An object rotating without any outside forces on it will have one stationary angular momentum vector. In order to have a precession of this angular momentum vector, torque must be applied. This torque added (integrated) over time will add to the current angular momentum vector to give the new angular momentum vector. In order for the angular momentum vector to always point towards (or away from) the sun the torque applied would have to be strong enough in magnitude that it could stop the planet rotation in quarter year. That might not be so bad except the direction the torque would be rather difficult to achieve. If you consider the axis of motion of the planet around the sun as up, then the torque would have to be pushing the bottom of the planet and pulling on the top. Unfortunately, since the planet is rotating, those halves are switching twice a day, so any gravitational pull would net do nothing, unless your day was really long (like if a day was equal to a year and thus the planet was tidally locked)

But there is another type of precession, a torque free precession where the axis of instantaneous rotation changes while the axis of angular momentum remains stationary. However, this could also not produce the desired movement as the two axis cannot point in opposite directions (or even be perpendicular) but in your described movement the axis of rotation points in completely the opposite direction every half year.

No

An object rotating without any outside forces on it will have one stationary angular momentum vector. In order to have a precession of this angular momentum vector, torque must be applied. This torque added (integrated) over time will add to the current angular momentum vector to give the new angular momentum vector. In order for the angular momentum vector to always point towards (or away from) the sun the torque applied would have to be strong enough in magnitude that it could stop the planet rotation in quarter year. That might not be so bad except the direction the torque would be rather difficult to achieve. If you consider the axis of motion of the planet around the sun as up, then the torque would have to be pushing the bottom of the planet and pulling on the top. Unfortunately, since the planet is rotating, those halves are switching twice a day, so any gravitational pull would net do nothing, unless your day was really long (like if a day was equal to a year and thus the planet was tidally locked)

But there is another type of precession, a torque free precession where the axis of instantaneous rotation changes while the axis of angular momentum remains stationary. However, this could also not produce the desired movement as the two axis cannot point in opposite directions (or even be perpendicular) but in your described movement the axis of rotation points in completely the opposite direction every half year.