The time that you can take the test depends on each individual engineering state Board. Most commonly, students can sit for the EIT exam in their final year in an ABET (Accreditation Board for Engineering and Technology) accredited Engineering program. Sitting for the exam at this time, though, is not required and you can take the EIT exam as late as you so desire. It is typically easier to get the exam done as close to the time of graduating due to the fact that the material being tested on is covered in the classes recently completed; however, taking the test while still in college in not required to pass the exam. Many individuals have taken and passed the exam and have gone on to become Professional Engineer’s after being out of college for a number of years.
See the State by State requirements page for more detail on when you are eligible to take the Engineer in Training exam.