可以使用与LWP相同的模块：

use AnyEvent::HTTP qw(http_get);
use HTTP::Message;
use HTTP::Headers;
use HTTP::Response;
my $can_accept = HTTP::Message::decodable;
http_get(
    "https://apa.at/",
    headers => { 'Accept-Encoding' => $can_accept },
    sub {
        my ( $body, $hdr ) = @_;
        delete( $hdr->{URL} );
        my $status  = delete( $hdr->{Status} );
        my $reason  = delete( $hdr->{Reason} );
        my $headers = HTTP::Headers->new(%$hdr);
        my $resp = HTTP::Response->new( $status, $reason, $headers, $body );

        print $resp->decoded_content . "\n";
    }
);

（来源：How can I accept gzip-compressed content using LWP::UserAgent?）