  The AcOH${}^+$ molecular ion is identified as a prospective system to search
for $\mathcal{CP}$-violation effects. According to our study AcOH${}^+$ belongs
to the class of laser-coolable polyatomic molecular cations implying the large
coherence time in the experiments to study symmetry violating effects of
fundamental interactions. We perform both nuclear and high level relativistic
coupled cluster electronic structure calculations to express experimentally
measurable $\mathcal{T}$,$\mathcal{P}$-violating energy shift in terms of
fundamental quantities such as the nuclear magnetic quadrupole moment (MQM),
electron electric dipole moment ($e$EDM) and dimensionless scalar-pseudoscalar
nuclear-electron interaction constant. We further express nuclear MQM in terms
of the strength constants of $\mathcal{CP}$-violating nuclear forces: quantum
chromodynamics vacuum angle $\bar{\theta}$ and quark chromo-EDMs. The
equilibrium geometry of AcOH${}^+$ in the ground and the four lowest excited
electronic states was found to be linear. The calculated Franck-Condon factors
and transition dipole moments indicate that the laser cooling using optical
cycle involving the first excited state is possible for the trapped AcOH${}^+$
ions with the Doppler limit estimated to be~$\sim 4$~nK. The lifetime of the
(0,1$^1$,0) excited vibrational state considered as a working one for MQM and
$e$EDM search experiments is estimated to be $\sim 0.4$ sec.

Atomic Physics;High Energy Physics - Phenomenology;Nuclear Theory