The typical household freezer is set to minus 18 C (zero Fahrenheit). Pure Rum shouldn’t freeze until the temperature falls to minus 27 C (-17 F), so it is safe in your freezer. Rum liqueurs have a lower ABV and therefore freeze more easily.
However, keeping Rum in the freezer is rare, as you typically want to be tasting it at its full potency and complexity, especially if drinking neat. In other words, if you’re planning on drinking that Rum neat, please do not stick it in the freezer, or it won’t be at its best when you sample it.