Yes, God uses even sinful acts by human beings to accomplish His purposes

CHAPTER 5: Of Divine Providence  (Part s One & Two)

God graciously created man upright and sinless.  God gave man His righteous law, which at that point contained only one prohibition: “Do not eat of the tree of the knowledge of good and evil.”  Had man kept instead of broken that law, he would have continued to live forever in perfect harmony with God in the Garden.  But God was so serious about man’s obedience that He wrapped the law in a threat:  “In the day you eat of it [the fruit from the forbidden tree] you shall surely die.”

Satan, the master of subtlety, used a serpent to tempt and overcome Eve, who then tempted and overcame her husband, Adam.

“Life or death?”  Our first father Adam, without compulsion, willingly broke God’s law, choosing disobedience and the promised subsequent death over obedience and life.

None of this was beyond God’s sovereign control.  God permissively decreed it in order to show His grace to mankind for His greater glory. (Ephesians 2:7)

 (Part Two)

The doctrine of God’s Providence instructs us that while God is the first cause of all things, and that all things He decrees will necessarily come to pass, leaving nothing to chance, God also providentially works through secondary causes.  Secondary causes include decisions and acts of sinful people—including sinful decisions and acts.  Almighty God is able, however, to even use these even these secondary causes to bring His will to pass, without being responsible for sin committed by those He created. 

A classic example is Christ’s crucifixion.  This greatest of all injustices ever committed was carried out by the hands of sinful people.  But according to Acts 2:23, it was also clearly the providential will of God by which He would forgive the elect of their sins.  What a comfort to know that God is in control of all things—including the sinful acts of people, for the purposes of His perfect will.