It doesn't sound natural to me.
The sentence structure, with Past Perfect and Simple Past, indicates that the action in Past Perfect (her calling you) was completed before the action in Simple Past (her saying something) began.
Now, whether this is true or not depends on the understanding of the word to call - in the context of communicating by phone, it can be understood as either initiating a conversation, or having a conversation. I think most people would lean towards interpreting "she called me" as "we had an entire conversation, from picking up the phone to hanging up", and as such, get the wrong idea about your sentence - that the entire call occurred before she spoke.
To me, you don't seem to need to emphasize that she called you (i.e. initiated a call) before she spoke, and if you just say:
She called me just now. She was saying...
no one is going to be confused about the ordering of the actions.