The answer to this question is a little bit problematic in that it has to rely on Biblical accounts that are, at times, not corroborated elsewhere.
With that caveat in mind, the first king of Israel was Saul, who is believed to have reigned from 1020-1000 BCE.
According to the book of 1st Samuel, the people of Israel asked God for a king. Samuel, the high priest, identified Saul as the man whom God had chosen for that position.
Samuel annointed Saul, thus making him the first king of Israel.
Please note that after Saul's time, Israel was often divided into two kingdoms -- Israel in the north, and Judah in the south.
It is supposedly King Saul.
As with all religious text, its authenticity cannot be cross-referenced as there are no more primary sources from that time.