There is no known cure for HIV nor AIDS at the moment. There are a lot of different kind of meds you must take daily to treat it, and nobody has found a cure for it. It can be fatal without treatment. If you take pills every day you can keep the HIV "virus load" very low and you can probably remain healthy.
In order to answer this, it is important that we understand the difference between HIV and AIDS.
HIV (Human Immunodeficiency Virus) is an incurable virus that can cause a life-threatening condition called AIDS (Acquired Immune Deficiency Syndrome). There is no immediate prospect of HIV becoming curable. AIDS is a syndrome (a collection of symptoms / illnesses) caused by the most advanced stages of HIV (Human Immunodeficiency Virus) infection.
AIDS is not an illness as such, but a person is said to have developed AIDS when their immune system is so badly damaged by HIV that it can no longer fight off a range of defined opportunistic infections. There is no known cure for HIV; so, although there are combinations of potent drugs that can help to keep the virus under control, none of them can completely get rid of the infection. In terms of CDC reporting, AIDS is an incurable condition .. BUT in that context AIDS simply means that a patient is HIV-positive AND has at some point either had a CD4 count below 200 per µL of blood, or has suffered from one of twenty or so AIDS-defining illnesses (it certainly does not mean that they are currently ill - and is therefore, in isolation, meaningless in terms of conveying a patient's current condition). With the exception of HIV itself, ALL the conditions / illnesses that lead to an AIDS diagnosis are potentially curable .. so whether or not you regard the condition of AIDS as being curable will very much depend on the exact definition you are employing, to what purpose the definition is being put and what country you are diagnosed in (the CDC definition is purely there for reporting purposes and is by no means a universal definition - indeed, very many countries no longer even use the term AIDS).
NOTE: Although HIV can be treated, it should be stressed that the drugs that are used are only fully effective in 80% of patients, are extremely expensive, all have unwelcome side effects, rely on a better than 95% accuracy in taking the correct doses at the correct time, are lifestyle limiting and still rely on you adopting a commonsense approach to keeping healthy. The drugs are not a quick fix solution and are not an excuse for complacency.