Sometimes in ice cores (ice cylinders that are mined by drilling ice) from Antarctica, layers of volcanic ash are found. These layers can rarely be seen with the naked eye - the presence of products of volcanic eruptions is determined by chemical analysis of ice.
In the ice of Antarctica, ashes of not only its volcanoes can be found - often ashes from volcanoes from Indonesia, for example, Tambora or Krakatau, are found in ice cores. But theoretically, ash can get to Antarctica even from Kamchatka, even from Iceland.
How does this happen?
If a volcanic eruption is powerful, then the products of the eruption enter the stratosphere (ten or more kilometers up) and are distributed throughout the globe - and fall out including in Antarctica. If the volcano throws ash into the troposphere (the lower atmosphere), then the ash cloud will settle, it will be washed away by rains, and it will not reach Antarctica.