According to the Online Etymology Dictionary,  the U.S. slang sense of salty meaning angry or irritated was first attested in 1938. On April 24th, 2007, an entry on the term was submitted to Urban Dictionary. The author describes it as having originated in Philadelphia, where it was defined as "looking stupid… because of something you did". It is thought to have entered into widespread usage on the internet through fighting game and multiplayer online battle arena (MOBA) communities.
On August 20th, 2002, an anonymous Urban Dictionary user submitted an entry regarding the term which describes a person who is pissed or upset. On April 22nd, 2006, Urban Dictionary user Shawn Maglicic submitted an entry regarding the phrase "Salty Bitch" which is described as one who is depressing, sad and overall dampens the mood of others. The term has become the subject of discussion on a number of gaming communities such as Marvel vs Capcom, League of Legends, Call of Duty, Tekken, and Street Fighter. On February 21st, 2014, Imgur user (source) uploaded an image titled "It's a little salty, but it'll do." which gained over 574.400 views and 3.340 points in a year.
On September 1st, 2014, Youtuber GRsmash began uploading a series of videos titled "Salty moments in smash" which highlights losing Smash Bros players during matches. The first episode (shown below, left) gathered over 340.800 views in 9 months. On October 29th, 2014, Youtuber KOSDFF tK uploaded a video which shows a Call of Duty Player raging over knife users in the game (shown below, right). The video gathered over 522.400 views in 7 months.
On Feburary 15th, 2015, Redditor Mountebank submitted question regarding the term on /r/answers which gained over 70 points (90% upvoted) and 30 comments in 4 months. The hashtag #Salty was adopted by users from Twitter, Tumblr, and Vine respectively.