I have 3 points: A, B, C  in 3D space. AC = BC in length. They represent a triangle object called T. Each point is a tuple of floats representing it's coordinates.
T is placed such as median point from A and B is in axes origin already.
In my API, I can rotate T globally, that is with respect to any one global axis at a time, for rotation.
Pseudocode for this API is like:
T.rotate('x', angle) for rotating T around global x axis of angle value, with right hand rule.
My question is for the code to rotate T such as: 

A and B are on x axis
C is on y axis

I suppose I will need 3 calls in succession, for rotating around each of the axes. But I have troubles figuring the angles by initial points coordinates.
EDITED to include angle calculations.
Since you do not provide any real code in your question, I'll just provide an algorithm and angles. If you improve your question with code I can add some code of my own.
To clarify, we must have length AC equal to length BC, and the midpoint of side AB must be the origin. That latter means that the coordinates of points A and B are negatives of each other. (Actually, the real requirements are that the vector OC where O is the origin is perpendicular to the vector AB and that origin is in line AB. Your conditions are more strict than this.)
Let's say that at any point the coordinates of A are (Ax, Ay, Az) and similarly for B and C.
First, move point A to the xy plane. Do this with a rotation of all three points around the x-axis. Due to the conditions, point B will also be in the xy plane. One possible angle of the rotation is -atan2(Az, Ay) though others are also possible. Check that the resulting values of Az and Bz are zero or close to it in floating-point precision.
Second, do a rotation around the z-axis to move point A to the x-axis (and the other points appropriately). Point B will now also be on the x-axis. One angle of rotation for this is -atan2(Ay, Ax). Check the resulting Ay and By.
Third and last, do a rotation around the x-axis to move point C to the y-axis. Points A and B will not be affected by this last rotation. One angle of rotation for this is -atan2(Cz, Cy). Check the resulting Cx (which should have been zero before this last rotation) and Cz.
Your triangle is now in the desired position, provided your original triangle actually met the conditions. Note that this algorithm did not use any rotation around the y-axis: it was not needed, though you could replace my initial rotation around x with one around y if you want.
Triangle rotation with Python