Short answer: No.
Longer answer: Definitely no! It took a Saturn V worth of energy to send a little spacecraft to the moon. To escape the sun's gravity well, it would take many orders of magnitude more energy. Plus enough energy to slow down and insert Erath into a circular orbit once you got to Alpha Centauri... So basically double the energy required.
It would be next to impossible to even eject a near Earth asteroid from the solar system due to the energy required.
That aside, there are other issues. The Earth rotates, so you'd have to stop it's rotation to keep the thrusters pointed in one direction. Also, Earth would rapidly turn into a frozen chunk of ice long before it ever passed the orbit of Jupiter.
The other thing is, if you put these thrusters on the surface, they would be dumping a
bunch of energy into the atmosphere, would cause many other problems, like heating the air to a plasma. Putting them above the atmosphere would require at least a 50 mile high tower strong enough to handle enough thrust to move a planet.
These are just the things I came up with off the top of my head, there are many, many more issues with this... questionable... plan.
In short, please don't try this! If you really want to see if it would work, either find an Earth no-one else is using at the moment, of build a craft in Orbiter with the size, mass, and inertia of a planet.