Can you start a sentence with the word anyway?

It's more acceptable in everyday writing. But for business and academic writing, reWord your thought and write it without "Anyway" as a sentence beginning. "Anyway" is a fluff or filler Word, similar to saying "you know". It often is not needed.

Informal:

I tried to tell the boy not to run on the ice but he wouldn't listen. Anyway, he fell, broke his leg, and I called the ambulance.

Formal:

I tried to tell the boy not to run on the ice but he wouldn't listen. He fell, broke his leg, and I called the ambulance.