I'm assuming here you're using <canvas>:
You can use the rotate function on the context to rotate any drawing functions. Draw the tiles with offsets around the centre, then post-translate them. Confusingly you write the translation first and it gets applied second, but here's how you'd do it:
var ctx = document.getElementById('your_canvas').getContext('2d');
ctx.translate(platorm_centre.x, platform_centre.y);
ctx.rotate(platform_angle);
ctx.drawImage( platform_image,
-platform_width/2, -platform_height/2,
platform_width, platform_height );
// Afterwards, go back to an identity transform:
ctx.setTransform( 1, 0, 0, 1, 0, 0 );
You can replace the single draw call with multiple draw calls to tiles if you subtract the platform's centre from the tile's world position.
Important to note is none of this applies to your physics to actually stand on the platform and make it tilt. I'm assuming you've already solved that problem. :)