Is there a resource that gives the number of citations per scientist in various countries?
There is a data set downloadable from SCImago. They used citation data from Scopus. Here is the ranking of the 50 countries with the most citations according to them (full list downloadable from their website; data are between 1996 and 2014). 

#  Country          Citations 
--------------------------
1  United States    177434935
2  United Kingdom   44011201
3  Germany          35721869
4  Japan            27040067
5  France           24700140
6  Canada           22152666
7  China            19110353
8  Italy            18019464
9  Netherlands      14278721
10 Australia        13772961
11 Spain            12628097
12 Switzerland      10872269
13 Sweden           9417604
14 South Korea      7063429
15 India            6989150
16 Belgium          6691791
17 Denmark          5494671
18 Israel           5079652
19 Brazil           5036027
20 Taiwan           4790230
21 Austria          4334382
22 Finland          4295721
23 Russian Fed.     4289618
24 Poland           3491958
25 Norway           3354827
26 Hong Kong        2951215
27 Turkey           2938841
28 Greece           2702414
29 Singapore        2561645
30 New Zealand      2495935
31 Portugal         2096242
32 Ireland          1999703
33 Mexico           1962572
34 Czech Republic   1867611
35 South Africa     1774278
36 Argentina        1681700
37 Hungary          1660840
38 Iran             1504541
39 Chile            1014687
40 Thailand         976328
41 Egypt            818728
42 Malaysia         670387
43 Ukraine          635570
44 Romania          619956
45 Slovenia         611672
46 Slovakia         561511
47 Saudi Arabia     547167
48 Croatia          459356
49 Bulgaria         455406
50 Pakistan         425467


Now it's unclear from the website how exactly they attribute a paper to a country when there are authors from multiple countries. Note also that, obviously, countries with many papers have many citations. It's fun to re-order the above list on the basis of citations by published paper:

#   Country          Citations per document
-------------------------------------------
1   Switzerland      26.1
2   Denmark          24.94
3   Netherlands      24.56
4   United States    23.36
5   Sweden           23.21
6   Canada           21.4
7   Finland          21.2
8   United Kingdom   21.03
9   Belgium          21.01
10  Israel           20.56
11  Norway           20.17
12  Australia        19.49
13  Austria          19.24
14  Ireland          19.01
15  New Zealand      18.52