  The dynamics of $\eta$-meson production and the interaction of $\eta$-mesons
with nucleons can be studied using the $\vec{p}p\to pp\eta$ reaction via
measurements of the analyzing power $A_{y}$. To this end, we have performed a
measurement of the $\vec{p}p\to pp\eta$ reaction using the
  WASA-at-COSY detector, which provides large acceptance and is
$\varphi$-symmetric. The experiment was carried out for beam momenta of $2026$
MeV/c and $2188$ MeV/c. In this article we present a method and results for the
determination of the degree of the beam polarization.
