Using a straw, poke a hole through the centers of the churros to hollow out a cavity for the filling.
On a plate, combine the cinnamon and the sugar and mix until it is a uniform color. Roll the hollowed out churros in the cinnamon sugar.
In a medium bowl, combine the cream cheese, confectioners' sugar, and vanilla, stirring until smooth. Transfer filling into a piping bag with a round tip and pipe the filling into the churros.