Specifically in this recipe: Tiramisu-II
The reason why I'm asking this is I only have vodka at home, and I rarely drink. So I don't want to buy any kind of liquor just for three tablespoons of it. Plus, alcohol is very expensive where I live.
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Rum used in tiramisu is mainly for flavor. It's not a fundamental ingredient that will completely change the outcome of the recipe.
That being said if you wish, you can omit the rum without adding the vodka. The vodka will add nothing to the tiramisu recipe since vodka is made to be flavorless.
As Jefromi mentioned in the comment, there are plenty of other better substitution in terms of flavor you can use. Kahlua is a very common liquor found in tiramisu as it's coffee based. Chocolate porters might also add a nice touch.
If you don't want to buy the alcohol but you have a good baking section in your local market or a nice baking shop, consider using the vodka for the alcohol content (just in case it does matter) and get the rum flavor using an extract.
You would probably need about one teaspoon or so, depending on how strong you want the flavor to be. You may also want to reduce the amount of vodka by the amount of extract you use.
I see rum extract or imitation rum quite a bit in the US, anyway.
You can also use almond extract (or a tiny amount of almond oil) if you prefer the amaretto flavor that some have mentioned. If you use almond oil you only need a few drops, usually.