In the (First) Apocalpyse of James, James asks Jesus "..Yet another thing I ask of you:who are the seven women who have been your disciples? And behold, all women bless you. I also am amazed how powerless vessels have become strong by a perception which is in them." Jesus then begins to list a number of "spirits". Much of the text is missing, but the names of the spirits are rather reminiscent of the Valentinian "daughters of Sophia". Later, Jesus gets back to the women, "When you speak these words of perception, encourage these four: Salome and Mariam (note: this is usally assumed to be Mary Magdalene) and Martha and Arsinoe.." much of the text is then missing...
That's the extent of the name Arsinoe. I've done various searches but have not found other references that could lead to clues.
She is mentioned briefly in two other texts. A Syriac fragment, hypothesized to be dependent on Tatians Diatessaron, tells a version of the empty tomb story in which an otherwise unknown Arsinoe joins Mary and Salome. The Manichean Psalmbook II 192.21 through 22 also includes Arsinoe along with Mary, Martha, and Salome as disciples of Jesus.
