What you want is called tracking. It's the overall spacing between the letters in a line.
I would center justify the text and adjust the tracking per line to space the letters out evenly. The fastest way is to highlight a line and use opt/alt with L/R arrows to track it out how you want it.
If some letters aren't looking evenly spaced to your liking you can fine-tune it by adjust the space between individual letters. That's called Kerning. You can do this quickly with the same keys above, but instead of selecting the whole line just place the text input cursor between the letters you want to kern.
Tracking and Kerning are also in the Character palette. You can enter smaller values of each than the quick keys increment.
When I first tried @Alin's answer it didn't work for me, but after getting down-voted I revisited it and it worked. My mistake was that I didn't make a text box and was working on a text line with hard breaks.
His method works well and is probably the easiest way to achieve what you asked for.