That's a good question. Viola does not strike me as particularly Petrarchan, as Romeo is ("I ne'er saw true beauty till this night!"), nor does Orsino overwhelm her with beautiful language. So what is it that establishes her love for Orsino?
Is she susceptible to flattery? Orsino compliments her lips, her voice, and her womanliness, although to us it's ironic because he's seeing a boy. But Viola is not that kind of fool for love, the type who could be won over by mere appreciation of her physique. To work, that requires a certain vanity. If anything, Viola is full of humility.
Yet, after Orsino explains his expectations for Cesario's surrogate wooing, Viola says, "Yet a barful strife! Whoe'er I woo, myself would be his wife." She's in love. How?
In our seminar at the Teaching Shakespeare Institute, we briefly considered one possibility. The following exchange occurs in Act 1, scene 2, between the recently shipwrecked Viola and Captain:
Who governs here?
A noble duke, in nature as in name.
What is his name?
Orsino. I have heard my father name him. He was a bachelor then.
Whoa, whoa, whoa. Say you're at a party and you see someone vaguely familiar across the room. You turn to your friend and ask who it is. When he tells you, which of the following are you most likely to ask?
a. Oh, I've heard of him; isn't he a Republican?
b. Oh, I've heard of him; doesn't he work at Home Depot?
c. Oh, I've heard of him; he's single, isn't he?
Viola's response is suggestive. Is she thinking about Orsino's availability already? Is she already in love with him? Add this: Under what circumstances did her father "name him"? We're too deep in speculation land here, with too little textual evidence, but comparing fathers and daughters' conversations in other plays, notably Romeo and Juliet and Hamlet, they often focus on appropriate husbands.
Then, there's the vaguery of Viola's plan. Originally, she wants to serve Olivia so that she "might not be delivered to the world/ Till I had made mine own occasion mellow,/ What my estate is." She wants to establish her social position, sure. But this position would also give her access to Orsino who, she learns, is currently seeking Olivia.
Finally, listen carefully to her instructions to the Captain:
Conceal me what I am, and be my aid
For such disguise as haply shall become
The form of my intent. (1.2.56-58)
What is her intent? No, what is the form of her intent? It would not be socially possible for her, as a woman, to approach Orsino in courtship. But disguised as a boy, taking on a new form, will give her access to Orsino. Is Orsino, then, as opposed to the mere establishment of social position, her intent? Or more specifically, is marriage to Orsino how she intends to make her own occasion "mellow"?
So, as we consider the origin of Viola's love for Orsino, we have to consider the possibility that we don't find it in the text, in the love-language, because it pre-dates the opening of the play.