Do the scriptures indicate the physical appearance of the Israelites? I have seen ancient depictions of the ancient Israelites and there features were different than I expected.

Linguistic experts have stated that Hebrew is one of the early Asiatic-African languages.

The Hamitic people were a dark skinned people, Noah's wife was Hamitic, moses' wife was Hamitic, the ancient Israelites mixed with Hamitic Egyptians for centuries before exodus.

In Acts 21:37-38 the soldier mistakenly took Paul for a Hamitic Egyptian. How could the soldier mistake Paul for an Egyptian unless the ancient Israelites were of a darker skin tone?

Is there any references in Scripture to the physical identity of the ancient Israelites?
We will literally never know without a time machine. However, given the region and it's history, as well as the people living there today it's reasonable to assert that they were a mix of all types of skin tones ranging from the typical Israeli today to the darker toned Northern African people today. 

The closest example to a "typical" Hamitic person is this picture of a Bashirin Hamite from Augustus Henry Keane's Man, Past and Present (1899). So if you went with Keane's findings, that'd be your closest answer. However, as I mentioned above, it's not unreasonable to assume they were the typical Israeli/Northern African tone.