Yes, the easiest way is to ensure the maximum width is 320px or less.
If you specify a larger header, then you’ll need some device-specific media queries in your CSS. Without knowing what size your header is, here is a starting point with comments to resize the header image based on screen/device size:
/* Tablet Portrait size to standard 960 */
@media only screen and (min-width: 768px) and (max-width: 959px) {
h1#site-title img {
max-width: 768px;
}
}
/* All Mobile Sizes (devices and browser) */
@media only screen and (max-width: 767px) {
h1#site-title img {
max-width: 320px;
margin: 0 auto;
}
}
/* Mobile Landscape Size to Tablet Portrait (devices and browsers) */
@media only screen and (min-width: 480px) and (max-width: 767px) {
h1#site-title img {
max-width: 480px;
}
}