Yes, God is a person. But, when we say that God is a “person,” we do not mean that He is a human being. We mean that God possesses “personality” and that He is a rational Being with self-awareness. Theologians often define person as “an individual being with a mind, emotions, and a will.” God definitely has an intellect (Psalm 139:17), emotions (Psalm 78:41), and volition (1 Corinthians 1:1). So, yes, God is a person.
No one doubts the personhood of man, and man is made in God’s image (Genesis 1:26–27). All through the Bible, the personal pronouns He, Him, and His are used of God.
The Bible teaches that God exists in three Persons: Father, Son, and Holy Spirit. The tri-unity of God is a difficult concept to consider, but the proof is in the Bible. In Isaiah 48:16 and 61:1, the Son is speaking while making reference to the Father and the Holy Spirit (cp. Luke 4:14–19). Matthew 3:16–17 describes Jesus’ baptism. God the Holy Spirit descends on God the Son while the Father proclaims His pleasure in the Son. Matthew 28:19 and 2 Corinthians 13:14 also speak of three distinct Persons in the Trinity.
God the Father is a Person with a mind (Isaiah 55:8–9), emotions (Psalm 78:40), and a will (1 Peter 2:15). God the Son is a Person with a mind (Luke 2:52), emotions (John 11:35), and a will (Luke 22:15). God the Holy Spirit is a Person with a mind (Romans 8:27), emotions (Ephesians 4:30), and a will (Galatians 5:17). All three Persons of the Trinity possess all the attributes of God (John 6:37-40; 8:17-25; Colossians 1:13-20; Psalm 90:2; 139:7–10; Job 42:2; 26:13; 1 Corinthians 2:9–11; Hebrews 9:14).
God shows His personal nature in that He expresses anger (Psalm 7:11), laughs (Psalm 2:4), has compassion (Psalm 135:14), loves (1 John 4:8), hates (Psalm 11:5), teaches (John 14:25), reproves (John 16:8), and leads (Romans 8:14). All of these actions imply the fact that God is a person.