No, “soul ties” are never mentioned in the Bible. Soul ties are said to be connections between two people’s souls, but the idea has no basis in Scripture.
However, the Bible does speak of close friendships. A good example is David and Jonathan:
After David had finished talking with Saul, Jonathan became one in spirit with David, and he loved him as himself. (1 Samuel 18:1)
In the King James Version, the verse reads
And it came to pass, when he had made an end of speaking unto Saul, that the soul of Jonathan was knit with the soul of David, and Jonathan loved him as his own soul.
This is simply old-fashioned language saying that Jonathan had a deep and committed friendship with David.