(Apologies for being slow in taking account of this important neologism.) Connor Adams Sheets, "What Is Capuling? 'Everyday I'm Çapuling' Turkish Protest Video Goes Viral", International Business Times 6/4/2013:
"Everyday I'm Çapuling!" is quickly becoming a rallying cry of sorts for the so-called "Turkish Spring" protests that have swept across Turkey since police violently broke up a protest camp in Istanbul's Taksim Square on Friday [May 31] with water cannons, tear gas and brutal violence.
Luke Harding, "Turkish protesters embrace Erdoğan insult and start 'capuling' craze", The Guardian, 6/10/2013:
When demonstrators first took to the streets to protest against the Turkish prime minister he branded them çapulcu, or looters. The word also means marauders or bums. But Recep Tayyip Erdoğan's attempt to demean his opponents has backfired. Protesters in Istanbul and other cities have embraced the word as their own, labelling themselves proud çapulcu and even coining an English verb, capuling.
Pronounced chapulling, with the emphasis on the second syllable, it has become synonymous with the alternative, youth-driven anti-Erdoğan movement. Students sleeping under the plane trees in Gezi Park, Istanbul, have dubbed their makeshift camp Capulistan, with many mounting cardboard signs next to their dwellings that read "Capul residence". Meanwhile, the city's must-have fashion accessory is a white T-shirt with the slogan: "Every day I'm capuling".
There's a Wikipedia article about the English neologism under the spelling "Chapulling". As noted in the article, and by Ben Zimmer in the comments, the original of the sound track is the "Every day I'm shuffling" segment of Party Rock Anthem by LMFAO.
One online dictionary glosses çapulcu as "looter, sacker, pillager, plunderer", with this pronunciation:
Another one gives the gloss "raider, depredator, freebooter, looter, marauder, plunderer, swag man", and offers the verb çapulculuk etmek meaning "maraud".
From another, we can learn that çapul means "booty, loot, plunder, the sack", while çapulculuk means "plunder, looting, sacking, pillaging, rapine".
Google Translate renders çapulcu as "marauder", with this synthetic pronunciation given:
Both in the pronunciations of the Turkish word, and in the English neologism as chanted in the video, it seems to me that the stress is on the first syllable, not on the second syllable as stated in the Guardian article. [As language hat observes in the comments, Turkish word accent is generally final, though this is consistent with some prosodic demarcation of initial syllables as well; in any case, I don't hear any evidence for the idea that stress is on the second syllable in the Turkish/English hybrid çapuling.]
In looking for other relevant dictionary entries, I found an online site for the Cambridge English-Turkish Learner's Dictionary, which offer an interestingly optimistic word cloud under the heading "Favorite Entries", presumably reflecting the things that most users have asked about most recently:
Here's hoping that this is an omen for the outcome of current events in Turkey. A more contentful note of optimism can be found in Soli Özel, "The protests in Turkey won’t be the last", WaPo 6/15/2013, or Louis Fishman, "The Gezi Park protests, the Middle East and the secular-religious divide", Zaman 6/16/2013.