How to rotate a 3D object on axis three.js?

Here are the two functions I use. They are based on matrix rotations. and can rotate around arbitrary axes. To rotate using the world's axes you would want to use the second function rotateAroundWorldAxis().

// Rotate an object around an arbitrary axis in object space
var rotObjectMatrix;
function rotateAroundObjectAxis(object, axis, radians) {
    rotObjectMatrix = new THREE.Matrix4();
    rotObjectMatrix.makeRotationAxis(axis.normalize(), radians);

    // old code for Three.JS pre r54:
    // object.matrix.multiplySelf(rotObjectMatrix);      // post-multiply
    // new code for Three.JS r55+:
    object.matrix.multiply(rotObjectMatrix);

    // old code for Three.js pre r49:
    // object.rotation.getRotationFromMatrix(object.matrix, object.scale);
    // old code for Three.js r50-r58:
    // object.rotation.setEulerFromRotationMatrix(object.matrix);
    // new code for Three.js r59+:
    object.rotation.setFromRotationMatrix(object.matrix);
}

var rotWorldMatrix;
// Rotate an object around an arbitrary axis in world space       
function rotateAroundWorldAxis(object, axis, radians) {
    rotWorldMatrix = new THREE.Matrix4();
    rotWorldMatrix.makeRotationAxis(axis.normalize(), radians);

    // old code for Three.JS pre r54:
    //  rotWorldMatrix.multiply(object.matrix);
    // new code for Three.JS r55+:
    rotWorldMatrix.multiply(object.matrix);                // pre-multiply

    object.matrix = rotWorldMatrix;

    // old code for Three.js pre r49:
    // object.rotation.getRotationFromMatrix(object.matrix, object.scale);
    // old code for Three.js pre r59:
    // object.rotation.setEulerFromRotationMatrix(object.matrix);
    // code for r59+:
    object.rotation.setFromRotationMatrix(object.matrix);
}

So you should call these functions within your anim function (requestAnimFrame callback), resulting in a rotation of 90 degrees on the x-axis:

var xAxis = new THREE.Vector3(1,0,0);
rotateAroundWorldAxis(mesh, xAxis, Math.PI / 180);

Since release r59, three.js provides those three functions to rotate a object around object axis.

object.rotateX(angle);
object.rotateY(angle);
object.rotateZ(angle);