Search public documentation:
The use of the UDK Logo and Trademarks is available to UDK developers to identify the UDK as their game’s engine and websites wishing to cross promote the UDK. If you are using the logo on a website you must make it link to www.udk.com. If a circumstance arises where you are unclear on logo usage direction, please submit materials to be approved in PDF format by email to Epic's engine marketing department representative – Dana Cowley (email@example.com). Please allow sufficient time for Epic to review and respond. A failure by Epic to respond does NOT indicate approval. You must receive actual approval from Epic games before proceeding.
UDK logo here: Download (Print and static software version logo for UDK)