Make a category my homepage

You can use pre_get_posts to ‘modify’ the main query to display posts from your specific category only. You will need to use the is_home() conditional to only target the home page of your blog.

The parameter cat that you are going to use in your query uses the category ID. You can also use the parameter category_name to display your category, just remember category_name is not the name of the category, but the slug of the category

You can add the following code to your functions.php. In this example, only posts from category 21 is displayed on the home page

function wpse_asc_cat_pages( $query ) {
    if ( $query->is_home() && $query->is_main_query() ) {
        $query->set( 'cat', 21 );
    }
}
add_action( 'pre_get_posts', 'wpse_asc_cat_pages' );

EDIT

Alternatively you can use WP_Query directly in your index.php to get posts from your selected category. You can change your loop to this

<?php
    $args = array(
    'cat' => 21
    );

    $the_query = new WP_Query( $args ); 

        if ( $the_query->have_posts() ) :
            // Start the Loop.
            while ( $the_query->have_posts() ) : $the_query->the_post();

                get_template_part( 'content', get_post_format() );

        endwhile;

    <---Pagination and rest of what you want to do--->      

    wp_reset_postdata(); 

?>