This passage is often cited as evidence that God ultimately decides which individuals will respond in faith to the gospel. I believe this is a misunderstanding of the text which has arisen in part through an accident of language.
Modern readers tend to associate the term “will” in Romans 9:16 with the concept of “free will.” Thus they hear in this verse an argument against the notion that salvation is ultimately conditioned on the response of faith, since that response is understood as an act of the will.
However, in Romans, the word “will” is never associated with the response of faith. In Paul’s grand exposition of the gospel, stretching from 1:16-8:39, this verb appears seven times. Every occurrence is in the following passage:
For what I am doing, I do not understand. For what I will to do, that I do not practice; but what I hate, that I do. If, then, I do what I will not to do, I agree with the law that it is good. But now, it is no longer I who do it, but sin that dwells in me. For I know that in me (that is, in my flesh) nothing good dwells; for to will is present with me, but how to perform what is good I do not find. For the good that I will to do, I do not do; but the evil I will not to do, that I practice. Now if I do what I will not to do, it is no longer I who do it, but sin that dwells in me. I find then a law, that evil is present with me, the one who wills to do good. For I delight in the law of God according to the inward man. But I see another law in my members, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my members. O wretched man that I am! Who will deliver me from this body of death? (7:15-24)
Notice that Paul never speaks of the man who “wills to have faith.” Paul speaks of the man who “wills to do good.” When Paul is speaking of “him who wills,” he is speaking of the person who is striving to keep God’s commands.
As we learn in Romans 7, such striving is futile. Our own will is impotent to deliver us from the slavery of sin. To be delivered from sin, we need to die and rise with Christ through the power of the Spirit (6:4-14, 8:10-11). It is the Spirit who fulfills in us "the righteous requirement of the law" (8:4), for by the Spirit “the love of God has been poured out in our hearts” (5:5), and “he who loves another has fulfilled the law” (13:8). Thus, “it is not of him who wills, nor of him who runs, but of God who shows mercy” (9:16).
And on whom has God chosen to bestow this mercy? Paul finds the answer in Joel 2:32: “Whoever calls on the name of the LORD shall be saved” (10:13). In other words, the mercy of God described in Romans 9:16 is available to all who simply believe in Jesus.
Faith does not require “will power.” It is not a striving or a fighting. It is not a work (4:5). Faith is simply the opening of oneself to the love of God revealed in Christ and mediated through the Holy Spirit.