Yes, you can knit in the summer time. Most people think knitting is just for the fall or winter seasons using heavy yarn, or wool. Not so! You can knit with cotton yarn, silk, rayon, and linen are some good choices. These yarns come in a variety of yarn weights and a price ranges.
Cotton makes a good choice for summer wear. It is light and absorbs moisture. So if you are out in the hot weather it will help to keep you cool by wisking away moisture.So try knitting a tank top or skirt. Here are a couple of great free patterns I found.