I know that practitioners of Japanese martial arts are called with a -ka ending (e.g. karate ka), but I wouldn't know how to denote a practitioner of Tai Chi Chuan or other Kung Fu styles. I recall asking a chinese friend who suggested that the term might have been Tai Chi Chuan su, but he wasn't even sure.
Do you know how to denote such a practitioner?
It depends on context, skill and time spent training.
If they just start training they're a student 学生(xué'shēng), when they become an official disciple they'll be called 徒弟(tú'dì).
Then when they become an instructor/teacher they'll be called 老师(lǎo'shī).
When they take on disciples of their own they'll be 师父(shī'fu) and when their skill is widely recognized as a master they can be called 师傅(shī'fù) or 高手(gāo'shǒu).
It is complicated in Chinese, and often depends on who is referring to whom, and what dialect is being used. In Japan, the term "-ka" is added (and in Korean "-in") to denote a "practitioner of". One equivalent in Chinese would be "jia", as in "Kung Fu-jia" or "Wushu-jia". The same character in Chinese for "jia" (家) is used in Japanese "ka", so I suspect this is the term you're looking for.
It could also be "xuesheng" which is used by itself and means "student".
There are several good answers here. I'll only add that there are specific names practitoners call other practitioners depending on relationship.
Very commonly utilized are the terms:
because all schools have longer-term, more advanced students who help teach the newer students.
If one is lucky, one also gains exposure to:
Many kung fu films involve the disciple seeking out their kung fu uncle or aunt for additional teaching. This can be extraordinarily valuable in getting a fuller picture of the art, particularly in regard to a certain style through existing relationships. (As an example, the founder of Bagua taught each of his disciples different things, based on their aptitudes, inclinations and body types. This is not at all uncommon.)
You can find a full list of martial relationship terms here: http://www.moyyee.com/about/kung-fu-terminology/
Regarding "Sifu", when addressing one's own teacher, one uses that term independently, or "Sifu [Name]". When addressing a master from another school, one reverses it: "[Name] Sifu". It's also fairly common for non-students to call any master "sifu" to show respect for their skill and/or reputation. In the same way, one can call a student from a different school "Si Hing" or "Si Jeh" to acknowledge the greater experience of that student.
Although there are uncountable schools (and famous rivalries) in the Chinese system, all practitoners are considered to be part of the jiānghú (江湖) or "gallant fraternity". It's important to understand these terms in the context of wuxia and of the Water Magin, one of the four great classical novels, in particular. (In the Water Margin, aka "Outlaws of the Marsh", the heroes are forced into outlawry, but are nevertheless virtuous. This idea was strongly reinforced by Li Jinglin ("Miracle Sword Lee") in the preface to The Major Methods of Wudang Sword, and is heavily emphasized in contemporary mythologization of martial heroes, most notably Wong Fei-Hung.
Essentially, all practitoners are part of one big family, and the familial nature of the terms referenced here is a reflection of that.
Adding on to Wigwam's answer, other options are
Although the last one translates to something like "Kung fu expert", I've heard it used as a respectful term for just practicioners of kung fu in general and it's probably the one I am most familiar with.
And for Tai Ji Quan specifically, I'd use
Since "拳击手" is the common name for "boxer".
I don't think there's a single proper term "kung fu/tai chi practitioner" but rather many for " -master" e.g. -大师 （dà shī），-高手 （gāo shōu）
By practitioner, I assume you mean someone who practices tài jì (taichi) regardless of skill level considerations.
As explained to me orally, and corroborated at least by the Wikipedia judoka description (which itself does not have a proper reference for this fact), the term judoka (柔道家) formerly referred to a practitioner with rank (3rd degree according to oral source, 4th degree according to Wikipedia), not a practitioner of any skill level. Thus, I think attempting to extrapolate jiā to a general practitioner is not a good idea.
Based on this interpretation of jiā, I would guess that 太极拳家 tài jì quán jiā has the same meaning as 太极门 tài jì mén, which is an inner door practitioner (disciple), not a practitioner of any skill level.
家 jiā is also used in 內家 nèi jiā, a term which comprises the internal martial arts.
A 学生 xuésheng student is usually used to describe someone who is insufficiently trained to be considered representative of the art, so also probably not what you are looking for.
I am not a native speaker of either Japanese or Chinese. I have found, however, that friends who are native speakers often do not know specialized martial arts vocabulary like nèi jiā.
