How to display Rate module widget by php
print rate_embed($node, 'plus1', RATE_FULL);

Here, first parameter($node) is the entity where you want to vote
'plus1' is the type of widget that you want to add
RATE_FULL is the display type of widget . Either it can be full or mini.

Try by passing $node =node_load(10). Where 10 is id of some node that exists in the site

Hope it will help