Can I file education tax credit without 1098-T tax forms?

In general, no. 

IRS says:

To be eligible to claim the American opportunity credit or the lifetime learning credit, the law requires a taxpayer (or a dependent) to have received Form 1098-T, Tuition Statement, from an eligible educational institution, whether domestic or foreign.

Please read this IRS publication page 1 for more information.

Yes, if you qualify for an exception. After telling TurboTax that you do not have a 1098-T, you will be asked if you qualify for an exception.  Answers yes.

 “However, a taxpayer may claim one of these education
benefits if the student doesn’t receive a Form 1098-T because
the student’s educational institution isn’t required to send a
Form 1098-T to the student under existing rules (for example, if
the student is a nonresident alien, has qualified education
expenses paid entirely with scholarships, or has qualified
education expenses paid under a formal billing arrangement). If a
student’s educational institution isn’t required to provide a Form
1098-T to the student, a taxpayer may claim one of these
education benefits without a Form 1098-T if the taxpayer
otherwise qualifies, can demonstrate that the taxpayer (or a
dependent) was enrolled at an eligible educational institution,
and can substantiate the payment of qualified tuition and related
expenses.”  https://www.irs.gov/pub/irs-pdf/f8917.pdf