Is there Scriptural Evidence that Moses had a command that made it Lawful for a Man to Divorce his Wife?

Examining two Gospel passages on the Teaching about Divorce:

Matthew 19:7-9 (RSVCE)
7 They said to him, “Why then did Moses command one to give a certificate of divorce, and to put her away?” 8 He said to them, “For your hardness of heart Moses allowed you to divorce your wives, but from the beginning it was not so. 9 And I say to you: whoever divorces his wife, except for unchastity, and marries another, commits adultery; and he who marries a divorced woman, commits adultery.”

and

Mark 10:3-5 (RSVCE)
3 He answered them, “What did Moses command you?” 4 They said, “Moses allowed a man to write a certificate of divorce, and to put her away.” 5 But Jesus said to them, “For your hardness of heart he wrote you this commandment.

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The Navarre Bible (Compact Edition) note re: Mk 10: 1-12:

This sort of scene is found often in the Gospel. The malevolent attitude of these Pharisees contrasts with the straightforwardness of the crowd, who are attentive to Jesus' teaching. Christ knows how two-faced his opponents are;that is why he asks them what Moses "commanded" (v.3). The Pharisees know that there is no such commandment, and therefore they reply that Moses "allowed" divorce (v.4). Having established the rules of dialogue, Jesus explains that the true commandment is what God established at the moment of Creation (Gen 2:24)[.]

[E]xcept for unchastity is better explained that if one enters into a marriage that is forbidden by God's Law, that marriage is not marriage at all in the eyes of God, and therefore an adulterous union.

A ready example in the Gospels is Herod who had 'married' Hero′di-as, his [Herod's] brother Philip’s wife. John was telling him put away Hero′di-as [because this is unchastity as] “[i]t is not lawful for you to have your brother’s wife.” cf. Mark 6:18 (RSVCE)

The short answer to your specific question is "No, no such evidence exists." But the question seems to be alluding to the conversation between the Pharisees and Jesus in Matthew 19. In that passage, the Pharisees asked why Moses "commanded" a man to give his wife a certificate of divorce and send her away. In his response, Jesus corrected the terminology saying it was not "commanded" but rather "allowed."

It is beyond the scope of your question, but it may be worthwhile (assuming this is truly a topic of interest to you) to study out the biblical difference between "divorcing" one's spouse and "sending away" one's spouse.

(Additional information per fredsbend's request)

There are two distinct words involved here. In the Old Testament there is the word "shallach" which means to "send away," "drive away," or "drive out." Its corresponding New Testament word is "apoluo." This means to "let loose" to "set free" to "drive out" to "send away." In the Old Testament again, "kerith uth" is a divorcement. The corresponding New Testament word would be a form of "apostasian" which is the actual document decreeing the dissolution of a union.

In English translations these terms tend to become blended, often being taken to mean same thing when they do not. We see this reflected in the KJV where we find Jesus speaking of divorce 10 or 11 times if you account for parallel passages. The KJV translates these words as "put away" in every case, with the singular exception Matthew 5, where the translators changed their approach and translated the 2nd occurrence as "divorce." I see no textual or contextual reason for this change.

In the Bible, both Old and New Testaments, there is only one recorded divorce, and that is in Jeremiah 3:8, where God said, "I have divorced Israel." This is the term "kerith uth" mentioned above. We know from reading the Bible and historical documents outside the Bible, that men regularly "put away" their wives. A man could tell his wife that she would see his face no more, and he would "put her away." He didn't divorce her, but just sent her off and chose to fulfill none of his husbandly responsibilities toward her.

So what we have in effect is "apoluo," the sending away, becomes "practical divorce" where "apostasian" is "legal divorce." The consequence of this is that we had men who were putting away their wives and marrying more women without ever granting their previous wives a legal divorce. Therefore the put away woman has no legal right to marry again. With that distinction in mind, read again what Jesus says in Matthew five. As you do so, remember that in every instance but one in that passage, the word is "apoluo" to "send away." We might rightly translate this "abandon," a man abandons his wife and goes off to marry a different one.

Jesus says, "...anyone who (puts away) his wife must give her a (certificate of divorcement)." If they don't, "...anyone who (puts away) his wife except for infidelity, causes her to commit adultery. And anyone who marries a woman who has been (put away) commits adultery." Why? Because it hasn't been legalized, or finalized. He is marrying a married woman.