Yes, it's possible. You can use a superconducting loop magnet. The power requirements are more or less zero, although you might need to use some power to keep the magnet cool, depending on the specific design.

However, the amount of protection the Earth's magnetic field provides is less than the amount of protection you really want. Earth's magnetic field isn't strong enough to protect against cosmic rays. In order to protect against cosmic rays, you'd need a stronger magnetic field.

On a different discussion group, I recall Luke Campbell calculating the mass requirements for such a superconducting magnetic field. The mass requirements ended up being less than the mass requirements for simple mass based shielding--but not by a whole lot. In practice, you'd do better with simple mass based shielding even though it would weigh more, because that shielding can be useful supplies (like big storage tanks for water/oxygen/food).