You should also consider keeping the dinucleotide composition by applying the Altschul-Erikson algorithm ("Significance of nucleotide sequence alignments: A method for random sequence permutation that preserves dinucleotide and codon usage", S.F. Altschul and B.W. Erikson, Mol. Biol. Evol., 2(6):526--538, 1985).

P. Clote already implemented it in Python for the community:

http://bioinformatics.bc.edu/clotelab/RNAdinucleotideShuffle/dinucleotideShuffle.html

There are countless ways to do this using pretty much any programming language.

From the perlfaq4: How do I shuffle an array randomly:

For example, if you either have Perl 5.8.0 or later installed, or if you have Scalar-List-Utils 1.03 or later installed, you can do the following from the command line (as a perl one liner):

perl -e 'use List::Util 'shuffle'; 
@original_dna = split(//, "ATATTCATGAGTACCGTA"); 
@random_dna = shuffle(@original_dna); 
print "\nOriginal: ", @original_dna, "\nRandom:   ", @random_dna, "\n\n";'

Based on answers from stackoverflow: shuffle string in python:

python -c "import random; 
dna=list('ATATTCATGAGTACCGTA'); 
print 'Original:',''.join(dna); 
random.shuffle(dna); 
print 'Random:  ',''.join(dna);"

You can use shuffleseq from the EMBOSS suite. Here's the documentation. Here's a web interface.

R version:

dna      = unlist(strsplit("acctg", split=""))
rand_dna = [sample(1:length(dna))]

Thanks for all the info above!!! All roads lead to Rome!