Rotating points on a circle

I have drawn a 2D circle in X,Y,Z. I wanted to draw something on specific vertices of that circle and I managed to do it. When I wanted to move the circle, I wanted the vertices to get the updated position, so I created another array of vertices and calculated the new vertex positions.

Now I want to rotate the circle, and while rotating it, the vertices should get the new orientation. How can I do this?

void creature::drawCircle(Vec3f Pos,float radius, int segments )
{

    // automatically determine the number of segments from the circumference
    if( segments <= 0 ) {
        segments = (int)math<double>::floor( radius * M_PI * 2 );
    }
    if( segments < 2 ) segments = 2;

    GLfloat *verts = new float[(segments+2)*3];
    GLfloat *vertsNew = new float[(segments+2)*3];
    verts[0] = 0;
    verts[1] = 0;
    verts[2] = 0;
    vertsNew[0] = 0;
    vertsNew[1] = 0;
    vertsNew[2] = 0;

    //Create circle
    for( int s = 0; s <= segments; s++ ) {
        float t = s / (float)segments * 2.0f * 3.14159f;
        verts[(s+1)*3+0] = math<float>::cos( t ) * radius;
        verts[(s+1)*3+1] = math<float>::sin( t ) * radius;
        verts[(s+1)*3+2] = 0;
    }

    //Transform points
    for( int s = 0; s <= segments; s++ ) {
    ci::Vec3f  m_newCirclePos;
        m_newCirclePos.x = verts[(s+1)*3+0];
        m_newCirclePos.y = verts[(s+1)*3+1];
        m_newCirclePos.z = verts[(s+1)*3+2];
        m_newCirclePos += ci::Vec3f(Pos);

        vertsNew[(s+1)*3+0] = m_newCirclePos.x;
        vertsNew[(s+1)*3+1] = m_newCirclePos.y;
        vertsNew[(s+1)*3+2] = 0;

    } 

    // Attach tentacles on specific vertices
    for (int i=0; i<m_tentacle.size(); i++)
    {
        m_tentacle[i]->m_Nodes[0].x = vertsNew[(i+1)*3+0];
        m_tentacle[i]->m_Nodes[0].y = vertsNew[(i+1)*3+1];
        m_tentacle[i]->m_Nodes[0].z = vertsNew[(i+1)*3+2];
        m_tentacle[i]->enforceConstraints(Vec2f(0,0),0,0,0,0);
    }
    glPointSize(10);
    glEnableClientState( GL_VERTEX_ARRAY );
    glVertexPointer( 3, GL_FLOAT, 0, vertsNew );
    glDrawArrays( GL_POINTS, 0, segments + 2 );
    glDisableClientState( GL_VERTEX_ARRAY );
    delete [] verts;
    delete [] vertsNew;
}