I have an iOS app written in Objective-c and a Wordpress Website with WooCommerce. How can I connect them?

Step 1) Install one of the plugins for Wordpress authentication. (P.S. I used basic authentication in the example below.)

Step 2) Go to WooCommerce > Settings > API > Keys/Apps, and add a new key and then generate API Key. It will create consumer_key and consumer_secret for you.

Step 3) Enable REST API in the WooCommerce settings. (To enable the REST API within WooCommerce, visit the WooCommerce > Settings > API tab and tick the Enable REST API checkbox.) source

Step 4) I assume that you are developing an app with Swift. If so see the code below for getting user details and orders for example. Don't forget to include Alamofire framework in your project.

// to get user infolet plainString = "WP_username:WP_password" as NSStringlet plainData = plainString.dataUsingEncoding(NSUTF8StringEncoding)let base64String = plainData!.base64EncodedStringWithOptions(NSDataBase64EncodingOptions(rawValue: 0))let headers = [    "Authorization": "Basic " + base64String]Alamofire.request(.GET, "http://yourwebsite.com/wp-json/wp/v2/users/me?_envelope=1&context=embed", headers: headers)    .responseJSON{ response in switch response.result {    case .Success(let JSON):        print("Success with JSON: \(JSON)")    case .Failure(let error):        print("Request failed with error: \(error)")        }}// to get a customer's ordersAlamofire.request(.GET, "https://yourwebsite.com/wc-api/v3/customers/USER_ID/orders", parameters:    ["consumer_key":"ck_XXX", "consumer_secret":"cs_XXX"])         .responseJSON{ response in switch response.result {            case .Success(let JSON):                let response = JSON as! NSDictionary                print(response)            case .Failure(let error):                print("Request failed with error: \(error)")          }}    

Well I don't if this is what you want but you could just put the website in a web view

You may want to look into the WooCommerce REST API. Sorry that I don't know if it offers everything you're looking for, but researching that might be a good starting point.