Have there been any successful studies showing that it is possible to increase IQ?
When talking about increasing intelligence there are a few things you have to keep in mind. Can you increase your IQ score? Probably, yes. Just take the same test twice, or more realistically practice a lot of IQ-type problems. You will probably raise a few points. 

But this is just a score. When experts are talking about raising intelligence, they are talking about raising the underlying ability that tests can only estimate. Raising your test score does not necessarily mean that you raised your intelligence. What you want is something that transfers over to some general ability.

Richard Haier, the editor-in-chief of the journal Intelligence, has written extensively on this topic. In his 2014 article Increased Intelligence Is A Myth (So Far) he writes about this very subject of increasing intelligence (Haier, 2014). You can probably guess what the conclusion is from the title of the paper. This topic is also a substantial portion of his book The Neuroscience of Intelligence (Haier, 2016).

Technically, when you ask whether there are any studies that purport to have found a way to increase intelligence, then the answer is definitely yes. There are many (hundreds, probably thousands). The correct question to ask is whether any of these ways consistently replicate. At the moment, the answer to this question appears to be no. One of the most infamous "ways of increasing intelligence" was the supposed Mozart Effect. The hypothesis was that listening to Mozart music would increase intelligence, and there were studies providing evidence for this. Fairly silly, yes. It was not until a meta-analysis came out of Mozart Effect studies that this hypothesis was finally laid to rest (Pietschnig et al, 2010). There is a history of many supposed ways of increasing intelligence being suggested, but typically the more scientific scrutiny they are put under they tend appear less and less impressive. Therefore, whenever a new way of increasing intelligence is suggested, it may be good to have some scepticism.

Given the current body of evidence, the most plausible way of raising intelligence is probably education (Ritchie &amp; Tucker-Drob, 2017). However, it is unclear whether education really increases general intelligence or just specific skills (Ritchie, Bates &amp; Deary, 2015).

The best  non-genetic way to get high intelligence is probably not to increase your intelligence per se, but just to avoid decreasing it. This means avoiding things like lead exposure, don't suffer from iodine deficiency (Qian et al, 2005), get decent nutrition and so on. Anything that realistically could interfere with the development of the brain may be implicated in intelligence.



See also my answer to a similar question on the Psychology &amp; Neuroscience Stack Exchange, which is slightly more comprehensive.