The elliptic flow of electrons from beauty hadron decays at midrapidity ($|y|$ $<~$ 0.8) is measured in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV with the ALICE detector at the LHC. The azimuthal distribution of the particles produced in the collisions can be parameterized with a Fourier expansion, in which the second harmonic coefficient represents the elliptic flow, $v_{\rm 2}$. The $v_{\rm 2}$ coefficient of electrons from beauty-hadron decays is measured for the first time in the transverse momentum ($p_{\rm{T}}$) range 1.3-6 GeV/$c$ in the centrality class 30-50%. The measurement of electrons from beauty-hadron decays exploits their larger mean proper decay length $c\tau \approx$ 500 $\mu$m compared to that of charm hadrons and most of the other background sources. The $v_{\rm 2}$ of electrons from beauty hadron decays at midrapidity is found to be positive with a significance of 3.75$\sigma$. The results provide insights on the degree of thermalization of beauty quarks in the medium. A model assuming full thermalization of beauty quarks is strongly disfavoured by the measurement at high $p_{\rm{T}}$, but is in agreement with the results at low $p_{\rm{T}}$. Transport models including substantial interactions of beauty quarks with an expanding strongly-interacting medium describe the measurement.