No. There is no such option for a few reasons.
Instagram announced they’re turning off the API and it never provided e-mail addresses, so you would not receive any valid contact information from your guests.
Instagram login has been used in the past, however it has never been providing user email addresses.
What’s more, the API is now deprecated and the new options do not include an authentication method. They even recommend that if you need an authentication solution, you should use Facebook Login instead. Check more about it here.