Unfortunately, no, you cannot (legally) take an itemized deduction for a Tennessee vehicle license tax or registration fee.
The legal reasoning is as
follows. The IRS only allows that portion of a state registration fee
that is based on the value of the vehicle to be included toward your
other itemized deductions. Any flat fee portion doesn't count. This
is why there are some 20+ states whose residents can potentially benefit from
the deduction; but the remainder (including Tennessee) cannot: these states do not charge
vehicle registration fees by value, and instead charge flat fees only, either by class or by category.
There is a list of
these qualifying states built-into the TurboTax software. A graphical
image of this chart of states is also shown in one of the screen-capture images
at the bottom of this answer (simply click to enlarge). Tennessee is not on the list, unfortunately.
If you purchase a new car in Tennessee, though, then any sales taxes you pay on it can count as an itemized deduction; but an annual registration tax / fee cannot, new car or otherwise.
Sorry be the bearer of these facts, but at least now you have accurate information with which to complete your tax return.
Thank you for asking this question.