It is possible. Though the term possible here means 'possible within our understanding of the laws of physics and will not violate fundamentals like conservation of mass' and not 'possible for the human race to do'. Let's talk orbital dynamics: [Side note: I'm just going to be using Sun instead of Sol, because this is mainly explaining the abstract concepts.]
All orbits are elliptical in nature (with one of the foci of the ellipse being the object in question, i.e. the Sun ), though most planet's orbits are fairly close to being circular that the change of distance between them and the Sun is somewhat insignificant. (In other words, Earth never leaves the Goldilocks zone.) There are six useful vectors when it comes to discussing moving orbits. The two most useful to us are prograde and retrograde. To get them, draw a tangent to the point where the planet is on the orbital plane. Prograde is forward, retrograde is backwards. (The other four vectors are to the sun / away from the sun, and north/south relative to the orbital plane.)
In other words, if you drew a cube around the planet, the directions we're interested in are the faces that correspond to the orbital path, not the vertical faces, nor the faces that point to the Sun.
See, orbital dynamics are a bit weird to jump to from plain old Earth kinematics. The reason being that exerting force to the Sun isn't a good way to make the orbit closer to the Sun. Reason being that if you tally up the vectors the planet already has, it already possesses a vector towards the Sun. It has to, otherwise it wouldn't be able to get to the far side of the Sun. (Would it work eventually? No, because you'd decay the orbit to the point were it wasn't stable.)
The way to reduce an orbit so that the object would have a closer orbit to the Sun would be to apply a retrograde vector. In other words, force applied opposite the direction the planet is going. This would directly reduce the orbit on the other side of the orbit. Remember, orbits are ellipses, not circles, so it's possible to have a somewhat non-standard orbit. So, if you took Mars as an example, you apply a retrograde vector at a point in Mars's orbit. (Preferably the apoapsis.) That would reduce the point in orbit 180 degrees away to Earth's orbit, assuming you applied enough force (and it'd be a lot). Then, half a Martian year later, when Mars reaches the 180 point, you apply force again, and reduce the orbit on the other side so now both sides are Earth-like.
As for applying the vectors - well, honestly, that's really hard to do without destroying the planet. I suppose as long as we're okay discussing these levels of energy, we can just Dyson sphere the planet, even though that's not typically what you'd use a Dyson sphere for, and apply the force to the Dyson sphere. Or possibly you apply a heat ray to specific portions of the atmosphere to turn it to plasma, replacing the atmosphere using comets as need be. But that seems like it could be another question entirely, I'm just spitballing here.
You may run into some more problems with orbits, given that Mars and Earth share a similar, but not identical, orbit plane. But that's what the other four vectors are for. A fine-tuning problem, if you will.