You could use a PHP widget
PHP Code:
<?php
$current_month = date('n');
switch ($current_month) {
case 1: echo '<a href="link1"><img src="/path/to/image1.jpg" /></a>'; break;
case 2: echo '<a href="link2"><img src="/path/to/image2.jpg" /></a>'; break;
case 3: echo '<a href="link3"><img src="/path/to/image3.jpg" /></a>'; break;
case 4: echo '<a href="link4"><img src="/path/to/image4.jpg" /></a>'; break;
case 5: echo '<a href="link5"><img src="/path/to/image5.jpg" /></a>'; break;
case 6: echo '<a href="link6"><img src="/path/to/image6.jpg" /></a>'; break;
case 7: echo '<a href="link7"><img src="/path/to/image7.jpg" /></a>'; break;
case 8: echo '<a href="link8"><img src="/path/to/image8.jpg" /></a>'; break;
case 9: echo '<a href="link9"><img src="/path/to/image9.jpg" /></a>'; break;
case 10: echo '<a href="link10"><img src="/path/to/image10.jpg" /></a>'; break;
case 11: echo '<a href="link11"><img src="/path/to/image11.jpg" /></a>'; break;
case 12: echo '<a href="link12"><img src="/path/to/image12.jpg" /></a>';
}
?>