The spaces are not the problem; your method of generating the query string is, as is your actual JSON payload.
Note that your original URL has a different JSON structure:
>>> from urllib import unquote
>>> unquote('%7B%22rajNames%22%3A%5B%22WAR%22%5D%7D')
'{"rajNames":["WAR"]}'
The rajNames parameter is a list, not a single string.
Next, requests sees all data in params as a new parameter, so it used & to delimit from the previous parameter. Use a dictionary and leave the ?jsonRequest= part to requests to generate:
headers = {'Accept': 'application/json', 'Authorization': 'Bearer '+access_token}
json_data = {'rajNames': ['WAR']}
params = {'jsonRequest': json.dumps(json_data)}
url = 'http://258.198.39.215:8280/areas/0.1/get/raj/name'
r = requests.get(url, params=params, headers=headers)
print _r.url
Demo:
>>> import requests
>>> import json
>>> headers = {'Accept': 'application/json', 'Authorization': 'Bearer <access_token>'}
>>> json_data = {'rajNames': ['WAR']}
>>> params = {'jsonRequest': json.dumps(json_data)}
>>> url = 'http://258.198.39.215:8280/areas/0.1/get/raj/name'
>>> requests.Request('GET', url, params=params, headers=headers).prepare().url
'http://258.198.39.215:8280/areas/0.1/get/raj/name?jsonRequest=%7B%22rajNames%22%3A+%5B%22WAR%22%5D%7D'
You can still eliminate the spaces used in the JSON output from json.dumps() by setting the separators argument to (',', ':'):
>>> json.dumps(json_data)
'{"rajNames": ["WAR"]}'
>>> json.dumps(json_data, separators=(',', ':'))
'{"rajNames":["WAR"]}'
but I doubt that is really needed.