Satan cannot perfectly read your mind, but no single passage in Scripture states this definitively.  We infer that Satan cannot read our minds for a number of reasons.  First, Satan is a created being, originally a powerful angel (see Ezekiel 28:13,14).  Though he aspired to be like God (see Isaiah 14:13,14), he is not God's equal in any way.  Only God has the ability to be everywhere — all present, all-knowing and all-powerful.  Therefore, only God has complete and continual knowledge of our minds' activities (see Psalm 139).
Second, everywhere in the Bible that angels or demons interact with people or God, information must be exchanged through communication. Certainly if Satan could have read Jesus' mind, he would have altered his doomed strategy in the temptations he devised (see Matthew 4:1-11).  Instead, the devil tries different temptations, and each time Jesus resists him verbally, using the sword of the Spirit as we are called to do (see Ephesians 6:17).
Third, in Daniel 2, King Nebuchadnezzar wisely demanded that his Chaldean sorcerers reveal the content of both of his dreams before interpreting them in order to validate the divine origin of the interpretation.  The sorcerers were stumped because they knew their normal sources of power and information (demons) could not read the king's mind.  Only God is the true revealer of such mysteries (see Daniel 2:11, 22, 28, 29, 47).  Certainly, if Satan had been able to read the king's mind, he would have been able to keep Daniel from advancing in the king's service.
What Satan can affect, apparently, is one's thought processes through the flesh.  He is, for instance, indicted for blinding the minds of the unbelieving (see 2 Corinthians 4:3, 4), and he darkens their understanding (see Ephesians 2:1-3 and 4:17-19). He and his demons can communicate false doctrine (see 2 Corinthians 11:13-15; Galatians 1:8; 1 Timothy 4:1; 1 John 4:1-3), and his demons can impact the thoughts of believers as well.  Satan is credited for prompting Ananias to lie to the Holy Spirit (see Acts 5:1-3), for moving David to consider his own strengths when he numbered the people of Israel (see 1 Chronicles 21:1, 2), for inspiring Peter's resistance to Christ's statement about His impending death (see Matthew 16:23), for inspiring worldly wisdom rooted in jealousy and ambition (see James 3:14,15; 4:7), and for leading minds away from devotion to Christ (see 2 Corinthians 11:3).  It isn't hard for Satan to know what you're thinking when he gives you the thoughts!
Furthermore, Satan and his demons use deception to give the impression they can read minds and know the future through divination and fortune-telling (see Acts 16:16,17).  Satan has also had opportunities since the beginning of creation to observe human behavior.  As a result, he has a thorough working knowledge of human behavior. He has learned what he must do to derive certain behaviors from the person he attacks.  He can also influence events by influencing key leaders.  He uses this deception to give the impression he is like God, able to read minds and control the future.  But remember that Christ has triumphed over Satan and, in Christ, you have the responsibility to resist him in submission to God.  When you do, he will flee (see Colossians 3:15; James 4:7).