A measurement of the elliptic flow (({v}{2})) of prompt (J/\psi ) mesons in high-multiplicity (p\text{Pb})collisions is reported using data collected by the CMS experiment at a nucleon-nucleon center-of-mass energy (\sqrt{{s}{\text{NN}}}=8.16\phantom{\rule{0.2em}{0ex}}\text{TeV}). Prompt (J/\psi ) mesons decaying into two muons are reconstructed in the rapidity region in the nucleon-nucleon center-of-mass frame (({y}{\text{cm}})), corresponding to either (-2.86<{y}{\text{cm}}<-1.86) or (0.94<{y}{\text{cm}}<1.94). The average ({v}{2}) result from the two rapidity ranges is reported over the transverse momentum (({p}{T}) ) range from 0.2 to 10 GeV. Positive ({v}{2}) values are observed for the prompt (J/\psi ) meson, as extracted from long-range two-particle correlations with charged hadrons, for (2<{p}_{T}<8) GeV. The prompt (J/\psi ) results are compared with previous CMS measurements of elliptic flow for open charm mesons (({D}^{0})) and strange hadrons. From these measurements, constraints can be obtained on the collective dynamics of charm quarks produced in high-multiplicity events arising from small systems.