If you would like to change your facebook profile picture with php or jquery. You can use below code for the same.

Please download facebook.js from Facebook SDK.

<script src="//code.jquery.com/jquery-latest.min.js"></script>
<script src="//connect.facebook.net/en_US/all.js"></script>
<script src="<?= BASE_URL ?>/js/facebook.js"></script>

// Additional JS functions here
    window.fbAsyncInit = function () {
        FB.init({
            appId: fbAppId, // App ID
            status: true, // check login status
            cookie: true, // enable cookies to allow the
            // server to access the session
            xfbml: true, // parse page for xfbml or html5
            // social plugins like login button below
            version: 'v2.0', // Specify an API version                   
        });

        // Put additional init code here
        FB.login(function (response) {
            if (response.status === 'connected') {
                console.info(response.authResponse);
                //alert("Your UID is " + response.authResponse.userID);
                // getFBData();
                UploadPicture(response.authResponse.userID);
                $('#fb_id').val(response.authResponse.userID);          

            }
        }, {scope: 'publish_actions,user_hometown,user_location,user_photos,user_videos'});
    };

    // Load the SDK Asynchronously
    (function (d, s, id) {
        var js, fjs = d.getElementsByTagName(s)[0];
        if (d.getElementById(id)) {
            return;
        }
        js = d.createElement(s);
        js.id = id;
        js.src = "//connect.facebook.net/en_US/sdk.js";
        fjs.parentNode.insertBefore(js, fjs);
    }(document, 'script', 'facebook-jssdk'));

    function getFBData() {
        FB.api('/me', function (data) {
            // alert(data.first_name + data.last_name + data.id);
        })
    }

 function UploadPicture(userid) {
        flag = false;
        var user_id = userid;
        var imgURL = "http://www.hdwallpapersimages.com/wp-content/uploads/2014/01/Winter-Tiger-Wild-Cat-Images.jpg";

        //change with your external photo url
        FB.api('/me/photos', 'post', {
            message: 'photo description',
            url: imgURL
        }, function (response) {

            console.info(response);
            if (!response || response.error) {
                console.info(response.error)
                return flag;
            } else {
                console.info(response);
                top.location.href = 'https://www.facebook.com/photo.php?fbid=' + response.id + '&amp;makeprofile=1';

            }

        });
    }