这是检查是否可以通过文件获取内容获取URL的好方法

if($url  = file_get_contents("https://api.twitter.com/1/statuses/user_timeline.json?screen_name=".$user)){}
else die("Invalid User");

Is this a good way to run this script?

I'm not sure what you mean, but if you ask if your call of file_get_contents is correct, then I must say yes, because, as stated here:

On failure, file_get_contents() will return FALSE.

Yes, your code is correct, and will fill $url with the contents of the page, or return false if the requested URL results in an error code. Note, however, that a page with a value of 0 or the empty string will also be interpreted as false. To avoid this, use the strong-matching !==:

if(false !== ($url  = file_get_contents("https://api.twitter.com/1/statuses/user_timeline.json?screen_name=".$user)))

If you just want to check that the URL is valid, use get_headers to only fetch the headers of the response with a HTTP HEAD request:

stream_context_set_default(
    array(
        'http' => array(
            'method' => 'HEAD'
        )
    )
);

$headers = get_headers('http://example.com'. 1);

// get the response code
$parts = explode(' ', $headers[0]);
$code = $parts[1];

if($code == 200) ... // success
if($code == 404) ... // failure

This will save you from transmitting the whole page over the network.

You need to check for === false (note the three =), since empty content or content 0 would also fail the test.

Better check the HTTP status code via the $http_response_header variable - it should be in the 200 range (200-299).