You do not need to have a federal Employer Identification Number (EIN) assigned, in order to be self-employed. You can operate your business, and file your tax returns under Schedule C (the main self-employment tax form), using just your Social Security Number (SSN).
That said, many self-employed persons voluntarily choose to apply for an EIN, rather than use their SSN for business, because they are concerned about identity theft and personal privacy. So, that is something that you may consider doing, if you are in a situation where you have to provide others your tax ID number for business reasons (like Form 1099s, sales tax invoices, business credit applications, etc.).
As a courtesy to you, here is a link to the (legitimate) IRS.gov webpage where you can learn about applying for a free EIN: