Scripture makes it crystal clear to us who is a Jew, and who is not:
Romans 2: 28 For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh: 29 But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God.
In the first century, there were those who claimed to be Jews, but were not. Jesus had these harsh words for them:
Revelation 2: 9... I know the blasphemy of them which say they are Jews, and are not, but are the synagogue of Satan. ("Satan" simply means "adversary", and it was a term used in the New Testament to refer to enemies of the gospel and God's people.)
In fact, to be a Jew, or part of "Israel," is to be a new creation in Christ:
Galatians 6: 14 But God forbid that I should glory, save in the cross of our Lord Jesus Christ, by whom the world is crucified unto me, and I unto the world. 15 For in Christ Jesus neither circumcision availeth any thing, nor uncircumcision, but a new creature. 16 And as many as walk according to this rule, peace be on them, and mercy, and upon the Israel of God.
Scripture also clearly identifies "the Seed of Abraham", to whom all God's promises belong:
Galatians 3: 7 Know ye therefore that they which are of faith, the same are the children of Abraham...16 Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many; but as of one, And to thy seed, which is Christ... 29 And if ye be Christ's, then are ye Abraham's seed, and heirs according to the promise.
Isaiah prophesied that when the Messiah came to redeem His people by forgiving their sins, Jerusalem would be called "The city of the LORD, The Zion of the Holy One of Israel" (Isaiah 60). Scripture tells us plainly and irrefutably that "the city of the Lord" and "Zion" is the church of Jesus Christ:
Hebrews 12: 22 But ye are come unto mount Sion, and unto the city of the living God, the heavenly Jerusalem, and to an innumerable company of angels, 23 To the general assembly and church of the firstborn, which are written in heaven, and to God the Judge of all, and to the spirits of just men made perfect, 24 And to Jesus the mediator of the new covenant, and to the blood of sprinkling, that speaketh better things than that of Abel.
So, regardless of your nationality, if you are a believer in Jesus Christ, you should feel free to call yourself a "Jew for Jesus". Or, to avoid superfluous redundancy, it would be entirely accurate to simply call yourself a "Jew"
Peace to you, the "Israel of God,"