Create a new custom tag in your tagmanager and paste this in. Add the html div to your page.

tagmanager-adsense-tag

<script>
  /*
     Replace the 'pub-xxxxxxxxxxxxxxxx' with your own Google Adsense publisher-id.
     Update the 'positions' with the data from your Google Adsense account page.

     Usage:
       <div class="tagmanager_ad" data-name="rectangle"></div>
   */

  var publisherId = "pub-xxxxxxxxxxxxxxxx",
    positions = [
      { 'data-name': 'rectangle',   'ad-slot-id': 1231231231, 'width': 336, 'height': 280 },
      { 'data-name': 'leaderboard', 'ad-slot-id': 2312312312, 'width': 468, 'height': 60  }
    ];



  // ========== Do not edit below this line ==========

  var ads = document.getElementsByClassName('tagmanager_ad'),
    found = false;

  for (var i = 0; i < ads.length; i++) {
    
    var adDiv = ads[i],
      name = adDiv.getAttribute('data-name');
    
    for (var pos in positions) {
      var position = positions[pos];
      if (name === position['data-name']) {
        found = true;
        adDiv.innerHTML = '<ins class="adsbygoogle" style="display:inline-block;width:' + position.width+ 'px;height:' + position.height + 'px" data-ad-client="ca-' + publisherId + '" data-ad-slot="' + position['ad-slot-id'] +'"></ins>';
      }
    }
  }

  (adsbygoogle = window.adsbygoogle || []).push({});

  if (found) {
    var script = document.createElement('script');
    script.type = 'text/javascript';
    script.async = true;
    script.src = document.location.protocol + '//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js';
    var s = document.getElementsByTagName('script')[0];
    s.parentNode.insertBefore(script, s);
  }
</script>