How to register nikkah in saudiarabia?

Since you reside in Saudi Arabia and wish to marry a US Green Card holder (a permanent resident of the United States), the procedures depend on each of your statuses (nationality, religion, and the groom's residency status).

1️⃣ Approval for Marriage to a Foreigner:

If one party is not Saudi, the "Foreigner Marriage Approval" required for Saudis is not usually necessary. However, the requirements for documenting a marriage between two foreigners in Saudi Arabia must be met, most importantly:
Valid residency permit for the party residing in Saudi Arabia
Passports for both parties
Certificate of marital status (single/divorced/widowed)
Premarital medical examination from an approved center in Saudi Arabia
Presence of two Muslim witnesses
Wife's guardian (if she is Muslim)

2️⃣ Performing the Marriage Contract in Saudi Arabia:

The marriage contract is performed by a licensed marriage officiant or through the court/Ministry of Justice portal (Najiz). After documentation, an official Saudi marriage certificate is issued.

3️⃣ Marriage Registration for US Immigration:

After the issuance of the Saudi marriage certificate, it must be:
Authenticated by the Saudi Ministry of Justice
Then by the Saudi Ministry of Foreign Affairs
Then registered/certified by the US Embassy
to become valid for use in immigration procedures (USCIS/Visa).

4️⃣ The Fiancé's Presence in Saudi Arabia:

Since he is a US permanent resident, he can enter Saudi Arabia on a valid visitor or tourist visa to complete the marriage, provided that his information and passport details match those on the marriage certificate.

In conclusion: You can legally complete the marriage in Saudi Arabia with an officially notarized contract, then have it authenticated abroad and use it later in immigration procedures to the United States. It is advisable to coordinate in advance with a licensed marriage officiant or a lawyer to prepare the documents before the December deadline.