The King James Version, among others, has made common the phrase “he is risen” in English.
The KJV has this phrase with the “he” occurring 6 times, and others identical in the Greek such as in Luke 24:6:
Mat 14:2 And said unto his servants, This is John the Baptist; he is risen (ἠγέρθη) from the dead; and therefore mighty works do shew forth themselves in him.
Mat 27:64 Command therefore that the sepulchre be made sure until the third day, lest his disciples come by night, and steal him away, and say unto the people, He is risen (ἠγέρθη) from the dead: so the last error shall be worse than the first.
Mat 28:6 He is not here: for he is risen (ἠγέρθη), as he said. Come, see the place where the Lord lay.
Mat 28:7 And go quickly, and tell his disciples that he is risen (ἠγέρθη) from the dead; and, behold, he goeth before you into Galilee; there shall ye see him: lo, I have told you.
Mar 6:16 But when Herod heard thereof, he said, It is John, whom I beheaded: he is risen (ἠγέρθη) from the dead.
Mar 16:6 And he saith unto them, Be not affrighted: Ye seek Jesus of Nazareth, which was crucified: he is risen (ἠγέρθη); he is not here: behold the place where they laid him.
See also Luke 24:6 He is not here, but is risen (ἠγέρθη) : remember how he spake unto you when he was yet in Galilee,
As we can see in each case both of John the Baptist and Jesus the Greek verb is ἠγέρθη, the Aorist Passive Indicative (and 3rd Person Singular) of egeirō. The verb which usually as an Aorist Passive means arise in any context, but often arise from sleep as in the case of the angel telling Joseph to arise and take the child to Egypt (Mat 2:13), and Joseph arising and doing so (14), but which is also used in arising from the dust, the sleep of death in resurrection. Aorist Passive here is what we would also in modern European languages call an intransitive use. Which compares to a transitive use where A does something to B, as for example when God can raise up (Aorist Active) from the stones children to Abraham (Mark 3:9).
This usage is consistent with what you would expect of someone who is risen, but the assumption is that they did not raise themselves but were raised by God or by Jesus. Here for example is the same verb, also in Passive Indicative but this time future about the Queen of the South:
Mat 12:42 The queen of the south shall rise up (ἐγερθήσεται) in the judgment with this generation, and shall condemn it: for she came from the uttermost parts of the earth to hear the wisdom of Solomon; and, behold, a greater than Solomon is here.
So clearly “he is risen” of Jesus or John the Baptist does not mean “he raised himself”.
To conclude this we should also look at where the English versions say God raised Jesus.
Acts 3:15 And killed the Prince of life, whom God hath raised (ἤγειρεν) from the dead; whereof we are witnesses.
Acts 4:10 Be it known unto you all, and to all the people of Israel, that by the name of Jesus Christ of Nazareth, whom ye crucified, whom God raised (ἤγειρεν) from the dead, even by him doth this man stand here before you whole.
Acts 5:30 The God of our fathers raised up (ἤγειρεν) Jesus, whom ye slew and hanged on a tree.
Here the same verb rise/raise is used in the Aorist Active Indicative (and 3rd Person Singular) as a transitive verb showing the grammatical subject (God) performing an action upon a grammatical object (Jesus). This is the same as the example mentioned above where God can raise up (Aorist Active) from the stones children to Abraham (Mark 3:9).
So the answer is that the Greek text says “he is risen”, not “he has been raised”, this is something we understand by context and other statements that God raised Jesus. So when we read those 7 statements at the beginning of this answer – about both John the Baptist and Jesus – the natural way to translate “he is risen” (ἠγέρθη) is “he is risen”, not as “he has been raised”. But the understanding of that is not a reflexive, John the Baptist or Jesus (or the Queen of the South) raised themselves.
Note:
The only reason why anyone could make an issue of it is due to misunderstanding of two more critical verses where Jesus appears to talk about having authority to receive back his life and raising the temple of his body in three days: Two related answers can be found at Does Jesus say he can raise himself “I have the power to give it up and the power to receive it back again” (John 10:18) and What did Jesus mean by “Destroy this temple, and in three days I will raise it up.”? (John 2:19) – in which for comparison the same verb again “I will raise” is in the Future Active Indicative (but 1st Person Singular).