Kay - «était reveillée» is the standard way in which passive voice is expressed:

Être (conjugated in simple tense in this case) - past participle - par

In this case, this is passive voice in the imparfait - she was habitually/regularly, or used to be, woken by the birds singing (not plus que parfait - that would be avait été reveillée ) 

Forming La Voix Passive with simple tenses in French (French Passive Voice)

 Forming La Voix Passive with compound tenses in French (French Passive Voice)

Hi Kay,

Is the action complete?

To write était réveillée seems appropriate to me, in the sense that the birds were singing  -- continuing past action, and she was woken by this action.

Hope this helps.

Jim

Thanks Jim, I must have been tired! Got it!