Clear WhatsApp's cache and data (from Settings > Apps > WhatsApp > Storage) and restart your phone. Next, try activating WhatsApp once again - and if you still don't receive any SMS code, you may request a phone call. If the problem persists, try reinstalling WhatsApp or test with a different device.
Once you've activated your account, that individual will be automatically logged out. You can then enable the two-step authentication to make your WhatsApp account secure. You can enable it by going to your WhatsApp settings, in Account > Two-step verification.