An exponential sum is a sum $\sum_{I=0}^{m-1} a_i \omega^I$, where $\omega$ is a primitive $m$th root of unity. We will show several examples of Tutte polynomial evaluations which are exponential sums. In particular, for a matroid $G$ representable over a finite field of order $q$, then the evaluation $q^{r(M)} \chi (G;q)$, where $\chi$ is the characteristic polynomial, can be written as an exponential sum in which the coefficients $a_i$ have an enumerative interpretation.