From the SFSRD (emphasis mine):
Anchoring Arcana (Su)
As a full action, you can make a single attack with a magic weapon against a single foe. ...
So if you have a magic weapon, you can make a special attack.
Rune of the Eldritch Knight (Su)
You can imbue a weapon with a magic sigil, the rune of the eldritch knight, allowing the weapon to act as a magic weapon for the purposes of bypassing DR and affecting incorporeal creatures. This takes 10 minutes, and you can imbue only a single weapon at a time. If you imbue a new weapon with the rune of the eldritch knight, any previously imbued weapon loses this benefit. When calculating the Hit Points and hardness of a weapon imbued with the rune of the eldritch knight, treat its item level as 5 higher.
So you can make a non-magic weapon count as a magic weapon.
Can a weapon imbued with Rune of the Eldritch Knight be used to make an Anchoring Arcana attack?
NOTE: A straightforward reading of the abilities would suggest that they can't be used together, since RotEK only makes a weapon count as magic for certain explicitly-defined purposes that do not include Anchoring Arcana. However it seems odd that soldiers would have an ability that requires a magic weapon and an ability that makes a weapon count as magic but that those abilities wouldn't work together. Therefore I am primarily interested in statements from the designers regarding whether these features are intended to work together.