I'm from Congo but I study in Tbilisi Georgia. I was in Ireland on a tourist visit but I was refused "permission to land" because they believed my "intentions for visiting Ireland were not genuine". The immigration officer said I had lied to him about my intentions for visiting Ireland; that some of the places which I intended to visit were either not tourist attractions or they weren't functioning anymore. So I was deported back to Tbilisi Georgia. But now I intend to reapply for the Irish visa again, this time for academic purpose. Will my visa application be granted or will it be refused because of the deportation?
It depends; there is no definite "yes" or "no" answer to this question. It might even depend only on the mood of the immigration officer who processes your new visa application.
In general, however, it is always best to be truthful in all aspects of your visa application (I'm not saying you weren't before, despite what they thought). That means that if the application asks "Have you ever been deported from or refused entry into any country", you will probably have to answer "Yes" (depending on what actually happened, as per Kate Gregory's comment). You will probably also have to explain the circumstances that led to your prior refusal. They will make a decision based on what you state and your prior history which they will have in their records.
Alternative: Get a tourist visa to the UK then go to Ireland.
The border between UK and Ireland is not often checked because the countries have a agreement (the Common Travel Area) that if you get into one you are allowed into the other. When I traveled by ferry from Holyhead to Dublin last year the Irish immigration desks were completely unmanned. I understand that the land border is even less policed than that! (At the airport however the Irish do check UK arrivals for passports).
So your easiest way may be to travel to England, then take ferry to Northern Ireland (part of the UK) for which no passport control is required. Then go by bus to Irish Republic.
When you apply for the UK tourist visa I don't think you will have a question about being refused entry to Ireland, just about being refused to UK. Which I assume the answer is no. So long as your paperwork showing strong reasons to return to Georgia is in order and the purpose of your UK tourism is valid you should get in ok.