It is so called неопределённо-личное предложение. Grammatically, it corresponds to English sentences with impersonal "they":
They speak four languages in Switzerland. - В Швейцарии говорят на четырёх языках.
They will sell a new model of this phone next year. - Новую модель этого телефона будут продавать в следующем году.
They are building a new bridge over the river. - Через реку строят новый мост.

As you can see, we omit "they" ("они") in these sentences in Russian, we just use a verb in third person plural.

So, literal translation is:
"Получающим российские паспорта предлагают давать клятву стране" - They offer to those who receive Russian Passports to take an oath to the country.