Some things to address: Because this is inverted syntax, there should be a comma after "to cheer you up" (assuming that the following corrections are taken into consideration).
To cheer you up, I am sending you a gift. (Why? Notice the way it is written when it isn't in inverted order: I am sending you a gift to cheer you up.) Personally, I prefer inverted word order in cases like these because it allows the part that would get less attention, to be front and center of the statement.