Can chewing on ice chips cause anemia?

No. Chewing ice chips can be a sign of being anemic (known as pica). It does not cause anemia. People with severe pica can be drawn to ingesting nonfood items such as clay, chalk, dirt, or sand. There are many people who chew ice and are not anemic. If you start chewing on chalk, however, go get a complete blood count.
No. There is an old wive's tale that chewing ice is a sign that someone may be anemic. But there is no way that chewing ice can actually cause anemia.