Now, after sticking to my guns with correct language use based of semantics, I need to make a caveat. I found an example of a certainly native-English-speaking corporation that uses the phrase "an offer can be applied" (though only once). It happens to be Amazon in its how-to for promotional codes. Note that when the process is described, the how-to shows where to enter a promotional code (not offer) and then click "apply." You can't enter an offer into a field. The phrase in question (the questionable phrase) appears further down amidst a whole lot of legalese. The thing is, the document specifically defines, for the purposes of the document, what the word "offer" will mean for the purposes of this particular document, and it's one heck of a intricate ball of attributes: "promotional claim code offer."
And where the "offer is applied", it is an example of catachresis, that is, a semantic error. It can be used by native speakers, sometimes as high literature—there it would be a deliberate "skewing" of the language landscape for poetic purposes, like the example in the Wikipedia article, "Mow the beard, Shave the grass."
This is not a reason, however, to expect a phrase like "My wife wants me to mow my beard" to be okayed for everyday use.
Which is why answers both on wordreference and here were suggesting to substitute something else either for "offer" ("promo code"), or for "applied" ("be used").
The correct semantics of this, I have detailed in the discussion to my previous answer.
An important factor in what to use in a language is established usage. Established usage is that it's the promo codes and the discounts that are "applied", overwhelmingly. The possibility of buying something with such a discount is an offer by a company, which is a meta-term, and it would be a semantic/stylistical mistake to use it metonymically.
The correct usage would be "This 20% sale is a nice offer by this company. You can take advantage of it by using a promo code. You apply it in your shopping cart when checking out".
Awkward language happens to all native speakers, especially when an intersection of legal matters and software use is involved.