Is there an API to create link categories programmatically?

wp_insert_link() allows you to set the category in the $linkdata args.

<?php
$linkdata = array(
    "link_id"       => 0, // integer, if updating, the ID of the existing link
    "link_url"      => '', // varchar, the URL the link points to
    "link_name"     => '', // varchar, the title of the link
    "link_image"        => '', // varchar, a URL of an image
    "link_target"       => '', // varchar, the target element for the anchor tag
    "link_description"  => '', // varchar, a short description of the link
    "link_visible"      => 'Y', // varchar, Y means visible, anything else means not
    "link_owner"        => '', // integer, a user ID
    "link_rating"       => 0, // integer, a rating for the link
    "link_updated"      => '0000-00-00 00:00:00', // datetime, when the link was last updated
    "link_rel"      => '', // varchar, a relationship of the link to you
    "link_notes"        => '', // text, an extended description of or notes on the link
    "link_rss"      => '', // varchar, a URL of an associated RSS feed
    "link_category"     => '' // int, the term ID of the link category. if empty, uses default link category
);
?>

This function does not create the link category it only assigns the link to category you specify (using the category id), so you will need to create all your link categories first then run your code to insert.

I would just set up all the links you want to import into arrays then run through them with a foreach loop.

$links = array(
    'Link Title' => array('http://example.org', 23 ),
    'Another Link Title' => array( 'http://domain.org', 17),
);

foreach ( $links as $key => $value ) {
   wp_insert_link( array( 'link_name' => $key, 'link_url' => $value[0], 'link_category' => $value[1] ) );

}