I dyed my hair. [If you did it yourself] I had my hair dyed / I got my hair dyed. [If someone else, a hairdresser for instance, did it for you.

You may want the word "dye".

It's "I dyed my hair". Or, if you did it very recently, like today, you can say "I've dyed my hair".

Simply you can say " I had colored my hair"

I dyed my hair.