No, because there's nothing like water for a keel to work against.
In water sailing there are two force vectors, the force vector from the reaction of the wind against the sail, adds toand the vector from the reaction of the keel (andand rudder) against the water, in propelling. These vectors add together to propel the sailboat. This works for almost any direction on the compass except where the wind is coming from, or about 45 degrees either side of that. "Beating close to the wind" as @geoffc mentions, is traveling up against that limit. "Tacking" is zigzagging - going for a while 45 degrees clockwise from the wind, and then for a while 45 degrees counterclockwise. Working your way upwind.
In solar sailing there's just one force vector, because there's only one medium, the solar photons, as @Craig mentions. With one vector the direction limits become more than 90 degrees to either side of where the sunlight is coming from. So no zigging, no zagging, using anything like tacking.
Now maybe gravity can be used as another vector via orbital mechanics as @Pearson and @SF mention, and maybe one day this will be called "tacking" but the physics are wholly different than a keel through water.
UPDATE, September 23rd 2017 issue of The Economist, p 73:
In some ways an E-sail [made of 20km-long tethers with a positive charge, repelling solar wind particles] resembles a solar sail, a rival idea for powering craft cheaply through space. A solar sail provides propulsion because the sunlight it reflects exerts pressure on the sail, pushing it forward. But E-sails have an important advantage over solar sails. Once unfurled, there is no easy way to stop a craft with a solar sail gathering speed. An E-sail-powered craft can be prevented from accelerating simply by switching off its electron gun. This means it can return to Earth under the influence of the sun's gravity.