Yes, you can apply for the rights shares even when you did not own any shares of the company as on record date. You can apply for the rights shares in the capacity of a renouncee based on the rights entitlements either purchased from the market or off-market.
The main criteria for applying to rights issue is having rights entitlement in your possession before the application is made. However, one thing to note in such a case is that the purchaser of the RE, i.e. the renouncee cannot apply for additional shares above their RE holding, unlike eligible shareholders as on record date who can apply for additional rights shares when subscribed to their rights in full.