I've googled go for a movie and I think that it is as same as go to a movie but it is less used. What is the difference in these two?
Go has different meanings.
(1) Go to a movie.
Definition 2: to move or travel, especially with someone else, to a particular place or in order to be present at an event
The idea of travel is included.
Other verbs-of-motion can be substituted:
walk to a movie; swim to a movie; run to a movie; roller skate to a movie; hop on one leg to a movie; crawl to a movie.
(2) Go for a movie.
Idiom: to choose to attend something
How about going for a movie? equals How about choosing to attend a movie?
(Note: this does not mean How about choosing a particular movie to attend.)
How about going for a fashion show? equals How about choosing to attend (go to) a fashion show?
Other verbs-of-motion may not be substituted:
*walk for a movie; *swim for a movie; *crawl for a movie
From The Great Gatsby:
Jordan suggests they go for a movie as Daisy signals them to pull alongside the coupé. She asks where they should go and Jordan again suggests the movies.
go for a movie = choose to go to a movie, instead of something esle
This is also not the same usage as such common phrases as:
go for a drive; go for a walk; go for a drink; go for a swim
While you can change them to:
go driving; go walking; go drinking; go swimming
but you can't really say
I'd like to discuss another possible context that hasn't been mentioned. "Go to a movie" is so much more popular because it is the standard way of saying you are seeing a movie.
For example, "I'm going to (go see) a movie tonight." You would never say "I'm going for a movie tonight."
So, when and why do we use "Go for a movie"? There's a phrase in English to express a desire for something: "I could go for X."
"I could really go for an ice cream right now." or "I could go for a nap."
This means, X sounds really good to me right now.
I would imagine "Go for a movie" being used in the following context:
"What do you want to do tonight?"
"I could go for a movie."
This is actually the only situation in which I can imagine using "Go for a movie." Another answer mentions the question "How about going for a movie?" I don't think this is wrong, but I've never heard before.
I would rather avoid saying "go for a movie" if you are suggesting to someone let's "watch a movie".
But when asked where are you heading off to, to say I am "going to a movie" is appropriate. It infers I am heading to watch a movie.