This answer depends on the definition of the word "free." Human beings unquestionably have a will, as we make decisions all the time. When the word "free" is added, however, it carries the idea of making a decision / taking an action with no outside influence or control. The Bible presents God as absolutely sovereign, in complete control of everything. Nothing can happen if God does not allow it. So, no, the human will is not technically free.
Does humanity truly have free will?
Even outside the sovereignty of God, there are other factors that restrict the will of humanity. The Bible teaches that we are all infected with sin, we all possess a sinful nature (Romans 3:23; 5:12). Sin prevents us from making truly free decisions. Sin plagues us to the very depth of our beings. Further, our wills are restricted by our own limitations. There are simply many things we are not capable of doing. We cannot choose to flap our arms and fly, for example. So, there are clearly multiple factors which prevent our wills from being completely free.
However, the lack of a truly free will does not lessen our responsibility for our own actions. We have the responsibility to choose rightly and wisely. In regards to our relationship with God and the salvation He offers, the Bible calls us to believe and change our minds (Matthew 3:2; Acts 3:19; 1 John 3:23). Every invitation to believe is a call to choose. An invitation to believe assumes the ability to choose to believe. We are without excuse (Romans 1:20-21) if we choose not to believe. We face consequences if we choose to take wrong actions (Galatians 6:7).
Do human beings have a will? Yes. Are human beings truly and fully responsible for their actions? Yes. Do human beings have the ability to make to make decisions completely free from all outside influences? No. How can we be fully responsible but not truly free? That is the mystery of existing in a universe with an absolutely sovereign God.
What is human nature?
The sin nature - What is it?
How do man's free will and God's sovereignty work together in salvation?
What does it mean that humanity is created in the image of God?
Why did God create humanity?
Truth about Humanity