Now a days opening a bank account in KSA is very simple. Especially AlRajhi and Alinma Bank offers their current accounts without Sponsor consent letter(NOC letter). Other banks may ask a No Objection Letter from sponsor.
For opening a current account with AlRajhi Bank just click this link and fill-up with your details, you will receive a SMS with your IBAN number within 24 hrs, then you can go to any of AlRajhi branch with your original Iqama to active your account. Usually within 7- 10 days they will issue your ATM card.
For opening a current account with AlInma Bank, just click this link and fill-up with your details, then you can go to the branch with your original Iqama, to activate the account. They will active your account and issue ATM card same day.