Hopefully, you are asking this question and not just throwing your corks in the garbage. Wine corks can be composted but there are some things to keep in mind.
First, a short rant on wine corks. Be sure that you are only buying wine that uses natural cork and not synthetic varieties. Natural cork is a sustainable natural resource that should be supported. Cork is harvested from the cork tree without killing the tree. As the bark of the cork tree thickens, the bark can be stripped off of the tree and no harm is done to the tree in the process. After 10 to 12 years the bark will be replenished and can be harvested again. The cork forests create natural green spaces, remove carbon dioxide, create oxygen and support the local economy. Again, be sure to always choose natural cork when you pick up a bottle of wine, for the reasons stated previosly and because it can be composted. Synthetic corks tend to have little use after being uncorked and tend to end up in the landfill where they will not break down, at least not for a very long time.
When it comes to composting cork there are some things to keep in mind. Cork is an impermeable material, so it doesn’t lend itself to being composted easily or quickly. Don’t drop an intact wine cork in your compost as it will take a long time to break down in that state. You’ll want to break up the cork in to smaller pieces. A good way of breaking up cork is to use a food processor to break the wine corks up into smaller pieces.
Once you have your wine corks broken up into smaller pieces you can either add the pieces to your compost bin or use them as a layer beneath soil to help with water retention where it’s needed. Adding the wine cork bits to the soil of your potted plants will reduce the rate of evaporation of water during hot summer days.