In the framework of the electroweak chiral Lagrangian, the one-loop induced effects of the anomalous $tbW$ coupling, which includes both left- and right-handed complex components, on the static electromagnetic properties of the $W$ boson and the $t$ quark are studied. The attention is focused mainly on the CP-violating electromagnetic properties. It is found that the $tbW$ anomalous coupling can induce both CP-violating moments of the $W$ boson, namely, its electric dipole ($\tilde{\mu}_W$) and magnetic quadrupole ($\tilde{Q}_W$) moments. As far as the $t$ quark is concerned, a potentially large electric dipole moment $(d_t)$ can arise due to the anomalous $tbW$ coupling. The most recent bounds on the left- and right-handed parameters from $B$ meson physics lead to the following estimates $\tilde{\mu}_W ~ 10^{-23}-10^{-22}$ e-cm and $\tilde{Q}_W~ 10^{-38}-10^{-37}$ e-cm$^2$, which are 7 and 14 orders of magnitude larger than the standard model (SM) predictions, whereas $d_t$ may be as large as $10^{-22}$ e-cm, which is about 8 orders of magnitude larger than its SM counterpart.