It is now possible to get US entry/exit records online. I just tried it and successfully got my travel history within a couple of minutes.
Here is the link to get you direct to the I-94 travel history request: https://i94.cbp.dhs.gov/I94/request.htmlIf you are a Non-immigrant U.S. visitor seeking access to your I-94 arrival/departure record for any point within the past five years, on May 1, 2014, CBP launched a new webpage that will allow you to retrieve this information without filing a FOIA requests. The portal will provide you access the date and port of entry of your arrivals and departures from the United States for the past 5 years.
When you visit http://www.cbp.gov/travel/international-visitors/i-94-instructions you can retrieve your I-94 arrival/departure record number and five-year travel history by entering your name, date of birth, and passport information.
Clicking on “Get Travel History” will return a five-year travel history based on the I-94 records, which you also can print.