You can change the object center for the text as well. If your curve origin is at the world origin, then the text origin has to share that same origin point. In your file, they do not, that’s why you are getting the distortion that you are seeing. Any offset from each objects’ origin creates a different result, that’s because the deformation is calculated from the objects’ origin point rather than the object its self.
To prove the point do this:
- create the curve (extrude out points in edit mode, but don’t move the entire curve around) this will place its origin at 0,0,0 on the world axes
- create your text (edit what is says if you wish) its origin will be at 0,0,0 as well
- apply the curve modifier to the text
- in object mode, move the text on the X axis and it will conform to the curve
Again, the important thing is that the objects’ origins occupy the same space at the beginning.