  The Antarctic Impulse Transient Antenna (\textsc{ANITA}) collaboration [1-3]
has reported two anomalous events with noninverted polarity. These events are
hard to explain in terms of conventional cosmic rays (CRs). We explore a new
possible explanation for these anomalous events by suggesting that these events
can be related to the dark matter (DM) annihilations within the so-called axion
quark nugget (AQN) DM model. This model was initially invented for a completely
different purpose to explain the observed similarity between the dark and the
visible components in the Universe, i.e. $\Omega_{\rm DM}\sim \Omega_{\rm
visible}$ without any fitting parameters. We investigate the signal properties
of the upward-going AQN events, including the event rate, the pulse duration,
and the electric field strength, and find them consistent with the
observations. We list several features of the upward-going AQN events distinct
from conventional CR air showers. The observations (or nonobservation) of these
features may substantiate (or refute) our proposal.
