At the moment, WordPress does not support to upload SVG and use SVG file. If you want to upload the SVG file into the WordPress media, you can add the following code to the functions.php file:

function cc_mime_types($mimes) {
$mimes['svg'] = 'image/svg+xml';
return $mimes;
add_filter('upload_mimes', 'cc_mime_types');

And now, you can upload the SVG file into the Media section.
To show your SVG file in the Logo section, you can use the following code in the functions.php file:

add_filter('get_custom_logo', 'dw_custom_logo_filter', 10, 1);
function dw_custom_logo_filter($html){
$image_url = 'YOUR_SVG_LOGO_URL';
$atl = get_bloginfo( 'name', 'display' );
$image = '<img alt="" src="'.$image_url.'" class="logo-color" alt="'.$atl.'" itemprop="logo">';

$html = sprintf( '<a href="%1$s" class="custom-logo-link" rel="home" itemprop="url">%2$s</a>',
esc_url( home_url( '/' ) ),
return $html;