Well, yes you still can!
Here are some points that will help you vote and elect your government despite being an NRI.
According to the provisions of the Representation of the People (Amendment) Act, 2010, a person who is a citizen of India and who has not acquired the citizenship of any other country and is otherwise eligible to be registered as a voter, can register as a voter in the constituency in which his place of residence in India as mentioned in his passport is located.
Electoral Rolls are also available on the website of CEO of concerned states
The NRI has to file the application for the purpose in prescribed Form 6A before the Electoral Registration Officer (ERO) of the constituency within which the place of ordinary residence of the applicant in India as given in his/her valid passport falls. The application can be presented in person before the ERO or sent by post addressed to the ERO concerned.
One recent passport size coloured photograph, photocopy of relevant pages of the passport of the applicant containing his/her photograph and all other particulars and photocopy of the pages of passport containing the valid visa.
If the application is sent by post, it must be accompanied by duly self-attested copy of the passport and all relevant documents mentioned in Form 6A. If the application is submitted in person before the ERO, the original passport should be produced for verification.
The registration details of the ERO will be communicated to the applicant by post on his address in the foreign country given by him in form 6A and also by SMS on the mobile number given by him in form 6A.
Electoral rolls are available on the website of the chief electoral officer of the concerned state concerned in PDF format and can be seen by anybody.
Once enrolled, an overseas elector will be able to cast his vote in an election in the constituency, in person, at the polling station provided for the part where he is registered as an overseas elector.
For more information, see the FAQs about registration