How to push both key and value into an Array in Jquery

There are no keys in JavaScript arrays. Use objects for that purpose.

var obj = {};

$.getJSON("displayjson.php",function (data) {
    $.each(data.news, function (i, news) {
        obj[news.title] = news.link;
    });                      
});

// later:
$.each(obj, function (index, value) {
    alert( index + ' : ' + value );
});

In JavaScript, objects fulfill the role of associative arrays. Be aware that objects do not have a defined "sort order" when iterating them (see below).

However, In your case it is not really clear to me why you transfer data from the original object (data.news) at all. Why do you not simply pass a reference to that object around?

You can combine objects and arrays to achieve predictable iteration and key/value behavior:

var arr = [];

$.getJSON("displayjson.php",function (data) {
    $.each(data.news, function (i, news) {
        arr.push({
            title: news.title, 
            link:  news.link
        });
    });                      
});

// later:
$.each(arr, function (index, value) {
    alert( value.title + ' : ' + value.link );
});

This code

var title = news.title;
var link = news.link;
arr.push({title : link});

is not doing what you think it does. What gets pushed is a new object with a single member named "title" and with link as the value ... the actual title value is not used. To save an object with two fields you have to do something like

arr.push({title:title, link:link});

or with recent Javascript advances you can use the shortcut

arr.push({title, link}); // Note: comma "," and not colon ":"

If instead you want the key of the object to be the content of the variable title you can use

arr.push({[title]: link}); // Note that title has been wrapped in brackets

I think you need to define an object and then push in array

var obj = {};
obj[name] = val;
ary.push(obj);

arr[title] = link;

You're not pushing into the array, you're setting the element with the key title to the value link. As such your array should be an object.