I found this post from back in 2006. From 1996-2006 they were ranked 31 in the world.
http://forums.sherdog.com/forums/f2/best-wrestling-countries-385529/
Here's a list of the best wrestling countries. Methodology used is medals won at the Olympics and World Championships in freestyle and greco-roman since 1996. 1996 was the first Olympic year that had all of the new countries from the former Soviet Union. Since then, 36 countries have won wrestling medals. Top five countries in order are: Russia, Cuba, America, Iran and South Korea.
This is a list of rank, total medals, total points based on 3 points for gold, 2 for silver and 1 for bronze and average weight in kg of medal winners. Rank tie breakers are based on gold, silver then bronze medals won.
rank, country, total medals, total points, average weight
1 Russia 77, 188, 85.9
2 Cuba 41, 79, 79.5
3 America 39, 77, 85.5
4 Iran 34, 68, 78.2
5 South Korea 31, 64, 64.9
6 Turkey 28, 56, 86.7
7 Bulgaria 23, 46, 69.7
8 Ukraine 25, 38, 73.4
9 Georgia 19, 34, 85.5
10 Uzbekistan 13, 30, 83.2
11 Kazakhstan 16, 30, 73.2
12 Hungary 16, 29, 92.8
13 Poland 12, 24, 80.0
14 Armenia 9, 22, 59.2
15 Sweden 10, 22, 86.9
16 Belarus 12, 21, 89.3
17 Azerbaijan 7, 17, 58.1
18 Germany 12, 17, 77.2
19 Canada 6, 13, 61.5
20 Finland 5, 9, 74.8
21 North Korea 6, 9, 55.7
22 Egypt 4, 8, 93.0
23 Israel 4, 6, 85.0
24 Japan 5, 6, 64.8
25 Mongolia 3, 5, 57.7
26 Romania 4, 5, 60.8
27 Macedonia 4, 5, 87.8
28 France 2, 4, 72.0
29 China 3, 4, 57.7
30 Greece 4, 4, 78.8
31 Moldova 2, 3, 92.5
32 Denmark 1, 2, 74.0
33 Turkmenistan 1, 2, 55.0
34 Czech Republic 1, 2, 97.0
35 Slovakia 2, 2, 72.0
36 Syria 1, 1, 54.0
