The Canadian dollar and the Norwegian krone are the liquid examples; the Russian rouble, the Mexican peso and several Gulf currencies belong to the wider family, though the Gulf states mostly manage the link away with a currency-peg instead.
The transmission is through terms-of-trade and the fiscal account. Higher crude means more export revenue and a stronger budget position, and in floating economies the currency absorbs part of the swing. The relationship is asymmetric in practice: crashes move currencies faster than rallies.
The mirror side matters too. Japan imports nearly all its energy, so a sustained oil rally weighs on the yen through the trade balance at the same time as it supports the loonie.
Example: crude falls from $85 to $65, a 23.5% drop. USD/CAD moves from 1.3400 to 1.3850, about 3.4% of Canadian dollar weakness, roughly a seventh of the oil move.
Related: commodity-currency, loonie, terms-of-trade, current-account