Can I create a field for entry of social security number that replaces the numbers with asterisks as they are entered?

That is not possible, we do not allow collecting sensitive credit card information: https://www.jotform.com/help/8-Terms-of-Use 

"Phishing. You agree that Company may terminate your JotForm Service immediately if a form's purpose is found to be deceptively obtaining: sensitive credit card information, social security numbers, user login credentials, or other sensitive personal information. All these activities are considered as Phishing and any account along with the violating forms will be suspended immediately."

Your account may get suspended immediately if you create such a form.