What the text says. At Antioch the prophet Agabus "signified by the Spirit that there should be a great famine over all the world: which came to pass in the days of Claudius" (Acts 11:28, ASV), and the disciples send relief to Judea.
The independent record. The famine is not known only from Acts. Josephus reports it twice. He describes Queen Helena of Adiabene, a convert to Judaism visiting Jerusalem, buying grain in Egypt and figs in Cyprus at great expense and distributing them to the starving, her son Izates sending money to the leading men in Jerusalem (Antiquities 20.2.5). And he places the disaster administratively: "Under these procurators that great famine happened in Judea, in which queen Helena bought corn in Egypt at a great expense, and distributed it to those that were in want", the procurators being Cuspius Fadus and Tiberius Alexander, which puts the famine in roughly AD 44-48 (Antiquities 20.5.2). Roman writers describe repeated shortages across the empire in the same reign: Suetonius records assiduous dearths and barren harvests under Claudius (Claudius 18), and Tacitus notes a scarcity at Rome (Annals 12.43), with Cassius Dio reporting hardship earlier in the reign (60.11). The 1915 ISBE already draws these together: "With the reign of Claudius is also associated the famine which was foretold by Agabus (Ac 11:28)", adding that classical writers report the reign as "a period of general distress and scarcity over the whole world".
What this shows, stated carefully. It does not show that a prophecy was fulfilled, that is a theological claim no document can settle. What it shows is smaller and checkable: the event Acts refers to is attested by writers outside the New Testament, including a Jewish historian and two Roman ones, and it can be dated. A modern reader can hold Acts 11:28 beside Josephus and read the same famine in two independent hands.
Sources: Acts 11:27-30; Josephus, Antiquities 20.2.5 and 20.5.2; ISBE 1915, "Claudius"; Suetonius, Claudius 18; Tacitus, Annals 12.43; Cassius Dio 60.11.
---