There is little reason to believe because the epistle is attributed to James that it really was written by James the brother of Jesus, or by another person called James. The author introduces himself merely as "a servant of God and of the Lord Jesus Christ", without invoking any special family relationship to Jesus nor claiming to have known Jesus personally, although such a claim would have assisted in presenting his arguments to the early Christian community.
Bart D. Ehrman says in Forged, page 198, says the one thing we know best about Paul's James of Jerusalem is that he was concerned that Jewish followers of Jesus continue to keep the requirements of Jewish law. This concern is completely and noticeably missing in this letter. This author, claiming to be James, is concerned with people doing good deeds, not with keeping kosher, observing the Sabbath and Jewish festivals or circumcision. His concerns are not those of James of Jerusalem. In other words, the letter is totally out of keeping with James, the brother of Jesus and the 'pillar' of the church in Jerusalem.
The New American Bible (NAB) discusses the scholarly view further , although without agreeing with it:
In addition to its Greek style, they [scholars] observe further that (a) the prestige that the writer is assumed to enjoy points to the later legendary reputation of James; (b) the discussion of the importance of good works seems to presuppose a debate subsequent to that in Paul's own day; (c) the author does not rely upon prescriptions of the Mosaic law, as we would expect from the historical James; (d) the letter contains no allusions to James's own history and to his relationship with Jesus or to the early Christian community of Jerusalem.
This leaves us to consider whether James the son of Zebedee or James the son of Alphaeus could have been the author. It always seems surprising when a disciple and intimate associate of Jesus writes an epistle without ever talking about his knowledge of Jesus and presenting arguments for a position without ever referring to the teachings of Jesus in support of those arguments. James only even mentions Jesus twice, at James 1:1 and James 2:1, and both verses are suspected of being later interpolations. The epistle is not about Jesus and relies on authorities other than Jesus, so could not have been written by a disciple of Jesus.
Add to those concerns that the author was not only skilled in Greek rhetoric, but used the Septuagint Old Testament. James the brother of Jesus in Paul's epistles and the two other James in the gospels would have used the Hebrew scriptures, if they were even able to read at all.
We do not know who wrote the Epistle of James, but it was neither James, brother of Jesus nor any of the disciples.