How can i read a Json file with a Azure function-Node.js

Here's a working example that uses the built in fs module:

var fs = require('fs');

module.exports = function (context, input) {
    var path = __dirname + '//test.json';
    fs.readFile(path, 'utf8', function (err, data) {
        if (err) {
            context.log.error(err);
            context.done(err);
        }

        var result = JSON.parse(data);
        context.log(result.name);
        context.done();
    });
}

Note the use of __dirname to get the current working directory.

There is a quicker way than @mathewc's. NodeJS allows you to require json files directly without the explicit read -> parse steps nor without an async callback. So:

var result = require(__dirname + '//test.json');