1-1/8 headtube goes with a 1-1/8 fork. The same goes for 1" HT and 1" fork.
Now, with that said, they do make "head tube reducers" - google search it and you will find plenty of options. Go for the 1-1/8 to 1" head tube reducer. I have never used this nor do I know of anyone who has used one so I cannot comment on the product.