Why did the God of the Israelites choose circumcision as a sign of his covenant? Has it anything to do with phallic worship?

It would be speculation to assess why God makes such capricious decisions. Perhaps as a sign of one's commitment to His calling or, more likely, a practical sanitary measure disguised as test of faith, though it is inflicted mostly on the unknowing who have no say in the matter. 

It has everything to do with asserting the possessors of male genitalia (men) as more worthy in God's eye. A fine example of the twisted Abrahamic perspective of human sexuality. An early lesson in body shaming. 

Ponder the metaphysical: If man is created in the image of God, does God HIMself have a foreskin? 

Acts 9:5 (KJV) reads, "And he said, Who art thou,
Lord? And the Lord said, I am Jesus whom thou persecutest; it is hard
for thee to kick against the pricks."

Circumcision was introduced to make those kicks less painful for the kicker.

No, it did not have anything to do with phallic worship. Circumcision, the “sign of the covenant” was a fitting symbol of pure worship marking those in covenant relationship with God a distinct people.

I don't know much about the topic so I had to do some searching. This is from a Jewish Rabbi

"We find G‑d on earth just as much (and perhaps more) than in the heavens. So we put a sign on the most physical and potentially lowly organ, to say that it can and should be used in a holy way. In fact, it is in sexuality that we can touch the deepest part of our soul—when we approach it with holiness."

This might be why the freemasons wear little white aprons over there holy of holies I don't know.

Apparently the practice was quite old and went back to ancient Egypt especially within the mystery religions. Here's a link

http://www.d.umn.edu/~mcco0322/history.htm

Still Abraham asked his servant to put his hand under his thigh when swearing an oath Genesis 24:2-9. Maybe this is where the Old testament and New Testicle comes from? Or when they say the magistrate has got them by the balls :)

"It would be speculation to assess why God makes such capricious decisions."

Well, that statement already contains an assessment and leads to another---that the sign of the covenant is an example both of the capriciousness of God and His intent to shame His very own creation.

I wouldn't believe in a god with those attributes either.

Once you decide God doesn't exist, you close a door and decide never to walk through it again.  At that point,  your ability to understand what is on the other side of that door is forever compromised---although you can always take the stance that anyone who has chosen to walk through that door and describe whatever he has found there could not possibly either exist or make sense if it did.

Those of us who decide that God does exist open the door, close it with conviction, and choose to learn everything we can about what's on the other side.  As we learn, we get insights and understandings about the reality on the other side that is unavailable to those who have not joined us there---or in some cases and for their own reasons have chosen to return to whence they came.

And that is the primary difference between an atheist and a theist---the theist cannot ever explain divinity to the atheist's satisfaction and the atheist cannot convince the theist that divinity does not exist.

But, Pea Nuts, here is one man's opinion.  He seems slightly embarrassed in retrospect by his answer, but I find it interesting:

www.thirstytheologian.com/2008/12/29/why_circumcision.php

(And Abraham was 99 years old when God told him this was the sign of the covenant.)

Who cares?

Why did this imaginary monster smite the

Amalekites?

No rhyme or reason with man made nonsense, just silliness!