Can I use Jynx's "Mimic" attack to draw cards from my deck when I don't have any cards in my hand?
Yes, but you must shuffle your deck first before you draw.
Source: HeartGold & SoulSilver FAQ (2010-02-11), PUI Rules Team (2010-02-11)

Relevant cards

Note: All applicable cards may not be listed below.
DP5_55
HGSS1_69