No, it's not available to home users, here are the requirements:
Who can use Microsoft Forms?
Microsoft Forms is generally available in all Office 365 Education suite licensing: Office 365 Education, Office 365 Education Plus, and Office 365 Education E5, as well as existing customers who purchased E3 prior to its retirement.
Microsoft Forms is available in Preview in the following Office 365 commercial suites: Office 365 Business Essentials, Office 365 Business Premium, and Office 365 Enterprise E1, E3, and E5 plans.
Simply log in to http://forms.microsoft.com with your Office 365 school or work credentials, and you can start creating surveys, quizzes, and polls.