What experiment for first time showed DNA is anti-parallel?
The definitive proof came with the crystal structure of B-DNA (see Watson &amp; Crick, 1953). Anti-parallel strands is the configuration that best explained the diffraction data while not violating chemistry (bond lengths and angles, no steric clashes, etc.).

The relevant sentence from the article is:


  the sequences of the atoms in the two chains run in opposite directions


I underlined this sentence in the following screenshot of the article: