Quote from Wikipedia article on camels:
Dromedaries may have first been domesticated by humans in Somalia and southern Arabia, around 3,000 BC, the Bactrian in central Asia around 2,500 BC,[14][62][63][64] as at Shar-i Sokhta (also known as the Burnt City), Iran.[65]
In accord with patriarchal traditions, cylinder seals from Middle Bronze Age Mesopotamia showed riders seated upon camels.[66]
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According to Wikipedia�s article on the Bronze Age: Middle Bronze Age (MBA) was 2100 - 1550 BC
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Abraham moved to Canaan from Ur, which was in Mesopotamia. There were not just domestic camels in Mesopotamia prior to 1550 BC; there were also camels that had been domesticated to the point of people riding them. So that�s one possibility for Abraham having camels.

However, the first mention of camels in the Bible was in Genesis 12:16, when Abram (who later became Abraham) was in Egypt:
Genesis 12:16 (NASB)
Therefore he treated Abram well for her sake; and gave him sheep and oxen and donkeys and male and female servants and female donkeys and camels.

When were domesticated camels first in Egypt? Egypt isn�t far from either Somalia or southern Arabia, where camels were domesticated around 3000 BCE. Could domesticated camels have been introduced to Egypt in the 1000 to 1500 years after camels were domesticated in Somalia and southern Arabia? Based on the evidence, there is no reason to doubt there were domesticated camels in Egypt in the period around 2000 to 1500 BCE, and that�s when and where domesticated camels were when first mentioned in the Bible.