The IRS offers e-Services which is a suite of web-based tools including Bulk TIN Matching. You apply for an e-Services account as an individual with a SSN, birthdate, address, phone number and last 8 digits of a Visa, Mastercard, or Discover credit card. The steps to applying for an e-Services account, with screenshots, is below.
Go to this page:
https://www.irs.gov/e-services
Scroll down and click on TIN Matching. Click on Access TIN Matching Application.
Your taken to a screen that looks like the following: