  Ramanujan's trigonometric sum $c_q(n)$ can be interpreted as a set of
trigonometric moments of a finite measure concentrated at primitive $q$-th
roots of unity with equal masses. This gives rise to sets of corresponding
polynomials orthogonal on the unit circle. We present explicit expressions of
these polynomials for special values of $q$, e.g. when $q=p$ or $q=2p$ or
$q=p^k$, where $p$ is a prime number. We generalize this procedure taking the
Kronecker polynomial instead of cyclotomic one. In this case the moments are
expressed as finite sums of $c_q(n)$ with different $q$.
