Yes, you can kayak in the rain. It is perfectly safe, provided you know the conditions that you will be paddling in and prepare yourself adequately. If you see lightning then get out of water.
Padding a kayak in the rain can be a wonderful and thrilling experience. However, you can only enjoy paddling in the rain if you are well prepared.
First, you need to carry the right gear to make your kayaking experience in the rain fun. This includes things like proper clothing, a reflector jacket to improve your visibility, a life jacket, and a spray skirt to help prevent the rain from entering your cockpit.
On a rainy day, there will be less people on lake, so you get more to yourself, and the fish are active so you have that benefit as well.
However, kayaking in the rain is not recommended for beginners who have little kayaking experience. It is ideal for pros who have adequate knowledge and expertise to judge the unexpected and make quick but wise decisions.