You can't sign up for Threads without Instagram. If you already have an Instagram account, you'll need to download Threads, sign in with your Instagram account, and then go through a couple of quick steps to create your profile. If you don't have an Instagram account, you'll need to first download Instagram and create an account.
One thing to note is you can't delete your Threads account without also deleting your Instagram account. But you can deactivate your Threads account and still keep Instagram.