Do the Chinese have text speak?
Short answer: yes. Skip to the last paragraph for a few examples.  
Long answer: it depends.
Firstly, the Chinese language is: 


isolating (low morpheme per word ratio)
written with characters


As you said, words used in English text speak are acronyms, i.e. made up from initial letters of some other words: 


  brb = be right back


In Chinese, characters are morphemes which are also words, therefore if text speak = acronyms (like imho, wrt), then there's very little room for it.

You do have sort of acronyms, or abbreviations, in Chinese. The most common occurrence is in lengthy names, for instance those of institutions, which comprise several two-character words. These are most of the times abbreviated using the most significant character from each distinct word. Example:


  (食品)药品监督管理局 (food &amp;) drug administration 
  becomes: 药监局



If text speak = word contraction, then yes, there are some forms commonly used in colloquial speech that eliminate bound morphemes:


  什么 > 啥  
  怎么 > 咋



Finally you can find some slang words used in written language that resemble more closely those you are talking about. Not real acronyms for the reasons stated above, but roman letters used in place of characters with the same pronunciation, which we can construe as examples of slang text speak in Chinese:


  
  p了 （bullshit!) -> letter p instead of 屁 (pi4) 
  sb (idiot) -> first pinyin letters of 傻逼 sha bi 
  wp (outsider) -> first pinyin letters of 外屁 wai pi, a distortion of 外地(人) used as a slur for non Shanghainese people in Shanghai.
  ooxx (having sex) -> letters o (read oh) and x (read cha as 叉 cross, same pronunciation as 插, insert/stick）