The trick is to hide the poster image and use the background as cover instead because the poster can't be rounded:
CSS:
video {
width:305px; //width or height can't be left out to keep aspect ratio
height:160px;
border-radius: 8px;
background:transparent url('your_poster_image.jpg') no-repeat 0 0;
-webkit-background-size:cover;
-moz-background-size:cover;
-o-background-size:cover;
background-size:cover;
}
HTML:
<video controls poster="transparent.png">
<source src="parrots.mp4" type="video/mp4">
<source src="parrots.webm" type="video/webm">
</video>
The transparent image can be download from here.