Is there a feat the allow Constructs to run?

[Sims]

Or do you have to "build" that into them?

[Flickerdart]

The Construct type does not bar a creature from running.

[Kuma Kode]

Creatures without Consitution scores are not prevented from taking the run action despite it being based on Constitution.

In fact, they can run indefinitely.

SRD - Nonabilities (http://www.d20srd.org/srd/specialAbilities.htm#nonabilities)

Constitution

Any living creature has at least 1 point of Constitution. A creature with no Constitution has no body or no metabolism. It is immune to any effect that requires a Fortitude save unless the effect works on objects or is harmless. The creature is also immune to ability damage, ability drain, and energy drain, and automatically fails Constitution checks. A creature with no Constitution cannot tire and thus can run indefinitely without tiring (unless the creature’s description says it cannot run).

[Vulaas]

However, if you want them to have the Run feat, you either need to make them intelligent so they can take it themselves, or make a custom magic item to give it to them.

[sonofzeal]

There is a Maug graft (Rollers, I believe) that do prevent running, but also give a huge boost to move speed so it doesn't matter as much.

[faceroll]

Creatures without Consitution scores are not prevented from taking the run action despite it being based on Constitution.

In fact, they can run indefinitely.

SRD - Nonabilities (http://www.d20srd.org/srd/specialAbilities.htm#nonabilities)

Huge boon for undead armies- move up to 12 times faster than living armies with the same move speed. Can also park them underwater for surprise attacks.