I receive json-files with data to be analyzed in R, for which I use the RJSONIO-package:
library(RJSONIO)
filename <- \"Indata.json\"
jFile <- fromJSON
Although your question doesn't specify this detail, you may want to make sure that loading the entire JSON in memory is actually what you want. It looks like RJSONIO is a DOM-based API.
What computation do you need to do? Can you use a streaming parser? An example of a SAX-like streaming parser for JSON is yajl.