Can I create the REST API of my application on azure and link them with laravel?

Yes, it's possible.

As Laravel doesn't have any built-in HTTP request package you may consider the following options to retrieve data from REST API.

• cURL

• file_get_contents

  $data = json_decode(file_get_contents('https://url_to_the_api'));
  

• Guzzle

  $client = new \GuzzleHttp\Client();
  $res = $client->request('GET', 'https://api.github.com/repos/guzzle/guzzle');
  echo $res->getStatusCode();
  // 200
  echo $res->getHeaderLine('content-type');
  // 'application/json; charset=utf8'
  echo $res->getBody();
  // '{"id": 1420053, "name": "guzzle", ...}'
  
  // Send an asynchronous request.
  $request = new \GuzzleHttp\Psr7\Request('GET', 'http://httpbin.org');
  $promise = $client->sendAsync($request)->then(function ($response) {
      echo 'I completed! ' . $response->getBody();
  });
  $promise->wait();
  

I personally prefer to use the Guzzle which can easily integrate with Laravel, you can check out @Mohammed Safeer's answer for details.