splice operates on array elements. 'ATCGC' is a string in Perl, not an array. A string can be converted into an array and operated on as such, but in this case it seems like a lot of wasted motion:

c:\@Work\Perl\monks>perl -wMstrict -le
"use Test::More 'no_plan';
 use Test::NoWarnings;
 ;;
 my $DNA3 = 'ATCGC';
 my @DNA3 = split '', $DNA3;
 ;;
 my $DNA4 = 'AAATTGC';
 my @DNA4 = split '', $DNA4;
 ;;
 my $offset = 1;
 splice @DNA3, $offset, 0, @DNA4;
 my $newDNA3 = join '', @DNA3;
 ;;
 is $newDNA3, 'AAAATTGCTCGC', 'array splice ok';
 ;;
 done_testing;
"
ok 1 - array splice ok
1..1
ok 2 - no warnings
1..2
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