Use INTERSECT with your parcels and your forest, then do a summary table that gives you total area for each parcel ID. This will be the the forested area. Then join that summary table back to the original parcels so that you can work with one record for each parcel. Calculate the percentage by diving forested area by original area.
Relative to the method in the comments on the original question, this saves you steps that will eliminate having to delete a large number of polygons in an edit session.
[Edit added later:]
There's an even better way, if you have an advanced license at version 10.3 or higher. It's the Tabulate Intersection tool. Your parcels would be the "zone" features and your forest polygons would be the "class" features. Make sure that your zone field is a unique parcel ID. "Class field" is optional, so if you don't supply one, presumably the whole forest layer will be considered all one class, which is what you want. The result will be a table with a record for each parcel ID, and the area and percentage covered by forest calculated for you. All in one step, just what you need.