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Dipavamsa VI 18 states (see page 43 in Oldenburg's work)
Asoko rajjam kâresi Pàțaliputte prurruttame,
Abhisitto tîņi vassâni pasanno buddhasàsane
Which roughly translates to,
Ashoka ruled in Pataliputra, best of towns, Three years after his coronation, he converted to Budhhism
So, yes there is a source.