Yes there is a reciprocal taxation agreement in place. You will pay 16% on your rental income (assuming you will be applying for a tax number in Romania) and 16% CGT in Romania. That's as a private investor. The rules are slightly different if you establish a romanian limited company.
Under the reciprocal tax agreement additional tax is payable to the Irish State adjusted to take into account what you have already paid in Ro.
I'm no tax expert so maybe others can elaborate on your liabilities at home.