Usually overshadowed by her older sister Cleopatra, Arsinoe briefly got a chance to shine during the Siege of Alexandria, when she killed Achillias and put her tutor Ganymedes in command of the Egyptian army, directly below herself. She proclaimed herself Queen and led the Egyptians to some successful against the Romans, trapping Caesar inside the city of Alexandria. However, her commanding officers exchanged her for Ptolemy XIII, her (twin? sources vary) brother and she was shipped off to Rome and was paraded in Caesar's triumph. Caesar then sent her to live out the rest of her days in the Temple of Artemis in Ephesus.
However, this isn't the end of her story. After Mark Anthony took control of the East, he gave Cyprus back as a gift to the Ptolemies, making Arsinoe IV and Cleopatra VII joint rulers of the island. Cleopatra saw this as a threat to her power, and organized her assassination.
Here's the POD. What if, Anthony turns a blind eye and lets her escape? She would probably seek to take back her throne, so she would probably seek refuge in a powerful nation that could oppose Rome. The logical candidate would be the Parthian Empire. Luckily for us, it just so happens that Parthia was about to send an army to invade the Roman East, under the command of Quintus Labienus, a Pompeian general, and Pacorus, the crown prince of Parthia. Arsinoe would perfectly fit into this plan, as she has a claim to the Egyptian throne, they could use her as a pretext to invade Egypt and place her as Queen, effectively making Egypt a Parthian vassal.
OTL, the army conquered Syria, killing the Roman commander in Syria, Lucius Decidius Saxa. The army then split up, with Labienus invading Asia Minor and enjoying great success there, being hailed as imperator and Pacorus invading the Levant and conquering all cities on the coast except Tyre, reaching Gaza and getting tribute from the Nabateans. In an ATL where Arsinoe accompanied the campaign, Pacorus would probably go further, invading Egypt. Pacorus was a great military leader, so I don't think capturing Egypt would be an issue.
What happens next? How would Rome react to this? For arguments sake, let's say Anthony dies and Labienus survives the campaign. How will the Parthians benefit from having the breadbasket of Egypt at their fingertips? Who will Arsinoe marry? Will Octavian still come to power?