There is an exceptional anagram generator at Anagram Genius. Simply type in the word or words you wish to be turned into an anagram and press 'Generate Anagrams,' and the Anagram Genius will produce an anagram for free. Type in 'reciprocity' and 'top icier cry' comes out!
The options on Anagram Genius include an emphasis of the anagram to be either satirical or flattering, or both. Gender is an option as is whether to include or exclude offensive words. There is also a tick box for business related words, so there really is a wide variety of options that the player can play with.
'Word-grabber.com' includes a Scrabble cheat where you place the letters from your Scrabble game into the generator and it produces several words that you can use in your Scrabble game.
'English-for-students.com' provides definitions of the different types of anagrams. An 'ambigram' is an anagram that is ambiguously opposite to the original phrase. Some descriptions of 'ambigrams' on the Internet state that an ambigram is an upside down word, but this is different to an anagram ambigram.
'Anagram List' provides some humorous anagrams such as 'a decimal point' - 'I'm a dot in place'. There is a lot to learn about anagrams and a lot of enjoyment to be had forming them.