One of the great selling points of fresh figs is that their flesh is so tender and delicate. Freezing will devalue your figs because it causes cell walls to rupture and produces a somewhat mushy texture in most thawed fruits. But, yes, you can certainly freeze figs.
The other issue you have to manage is that figs, like apples, apricots, and peaches, are particularly prone to discoloring. So you need to treat them with an acid to keep them looking good. This can be a thawed frozen fruit juice concentrate, such as orange, cranberry, or lemon juice, or a mixture of 1/2 teaspoon of ascorbic acid (vitamin C) dissolved in a quart of water. This treatment can alter the flavor of the fruit. Ascorbic acid, especially, can be bitter, though you might appreciate a lemon or orange hint in your figs.
To freeze figs, wash them and remove the stem. Peel them if you like. They can be sliced or frozen whole. Dip them in the acid wash and either pack them directly in a container for freezing, or freeze them separately on baking sheets and then pack the frozen figs in an airtight container.
Another alternative is to freeze the figs in syrup. Make a sugar syrup with 3 cups of sugar and 4 cups of water, heat to a boil, and then chill it thoroughly. Or mix 2 cups of a mild honey with 3 cups of warm water, blend them thoroughly, and chill. Then pack your figs in a container and cover with the syrup, leaving a half-inch to an inch of room at the top for expansion. A benefit of wet-pack freezing, is that you can add the lemon juice to inhibit discoloration to the syrup and skip the dipping step in the process.
You may also want to read: Freezing Food: A Complete Guide with Everything You Must Know