In general, you are supposed to apply in the country where you reside (not necessarily your country of origin or homeland). A one-month visit to Romania does not make Romania your country of residence, so you cannot apply there.
This is controlled by Article 6 of the Schengen Visa Code. The article does allow for exceptions:
Consular territorial competence
An application shall be examined and decided on by the consulate of the competent Member State in whose jurisdiction the applicant legally resides.
A consulate of the competent Member State shall examine and decide on an application lodged by a third-country national legally present but not residing in its jurisdiction, if the applicant has provided justification for lodging the application at that consulate.
Unfortunately for you, the visa processing handbook (available, for example, at https://www.udiregelverk.no/en/documents/schengen/16202010/) makes it clear that the "justification" must be some circumstance that prevents you from applying for the visa in your country of residence during the three months before you plan to travel to the Schengen area. If you have a good reason to explain why you were unable to apply for a Schengen visa in March, April, or May, then the a Schengen consulate in Romania might accept your application.