Is it possible to create a Google sign-up form accessible via iPhone etc. without the need for a Google account? We find we can open from a computer but not a phone if you don't have an account.
Is your issue that you do not want the creator of the form to need a Google Account or is the issue that you do not want the people submitting a form to need a Google Account?
If you do not want the creator to need a Google Account, you are out of luck but there is not really a purpose to this because then you would not be able to see responses.
I am guessing that your issue is that you do not want the submitters to need a Google Account. This is an easy fix. Simply go to the form's settings and uncheck this option and users will not be required to log in to submit the form.
More information on getting started can be found here.