The Arab population in Algeria arrived over several centuries, not in a single migration.
Here's the broad history:
Arab conquest (7th century CE): Arab Muslim armies from the Arabian Peninsula, mainly from the regions of today's Saudi Arabia, entered North Africa beginning around 647 CE. They brought Islam and the Arabic language. The conquest of much of present-day Algeria was completed over several decades after resistance from local Berber (Amazigh) kingdoms.
Settlement: Some Arab tribes settled in Algeria, especially in towns and fertile regions, but initially they were a minority among the indigenous Amazigh population.
Banu Hilal and Banu Sulaym migrations (11th century): Much larger numbers of Arabs arrived later. These nomadic tribes migrated from Egypt into Libya, Tunisia, Algeria and Morocco. Their migration greatly expanded the use of Arabic and Arab tribal culture across the countryside.
Today, most Algerians have mixed ancestry. Many people who identify as Arab have both Amazigh (Berber) and Arab ancestors due to centuries of intermarriage. Culturally and linguistically, many Algerians are Arabized, while others continue to identify primarily as Amazigh and speak Amazigh languages.
The original Arab settlers came from the Arabian Peninsula.
Large tribal migrations later came via Egypt.
Modern Algerian Arabs are generally the result of centuries of mixing between Arab migrants and the indigenous Amazigh population.