I have made that claim and different people asked me for the sources.
(50% is obviously a rough gage, nearer to 2/3rds in Muslim countries, nearer to 1/3rd in the West)
So, here is the best info I gathered on the subject in this one thread. I welcome any better data.
Muslim-majority countries
http://www.pewforum.org/2013/04/30/the-worlds-muslims-religion-politics-society-overview/
Support for Sharia is well over 50% in Asia (Indian subcontinent and Malaysia/Indonesia), the Middle East ('Arab' countries, Iran not polled) and Africa (Maghreb and Sub-Saharan Africa)
It is below 50% in the mostly ex-Communist region roughly between Turkey and Russia (incl. Kemal's Turkey)
UK: 40% Muslims support Sharia (2006)
http://www.telegraph.co.uk/news/uknews/1510866/Poll-reveals-40pc-of-Muslims-want-sharia-law-in-UK.html
http://www.icmunlimited.com/pdfs/2006_february_sunday_telegraph_muslims_poll.pdf
The question asked being: "How supportive, if at all, would you be of the official introduction of Shari'ah Law into British law for Muslims in Britain?"
Very supportive - 21%
Fairly supportive - 19%"
US: 33% Muslims support Sharia (2015)
https://www.centerforsecuritypolicy.org/2015/06/23/nationwide-poll-of-us-muslims-shows-thousands-support-shariah-jihad/
The Center for Security Policy is Conservative, but the whole study report is presented
Question #8
"If Sharia conflicts with the US Constitution and the Bill of Rigts, which law should be considered supreme?"
The US Constitution - 43%
Sharia - 33%
dk+na - 23%"
Germany: 34 to 45% support for Sharia (2007)
(academic study for Ministry of Interior)
http://www.bmi.bund.de/cae/servlet/contentblob/139732/publicationFile/14975/Muslime%20in%20Deutschland.pdf
Long study, no specific question on Sharia, some pointers:
45% of German Muslims agree "only Islam is able to solve the problems of our time" (p. 120, Table 12)
34 % of German Muslims agree violence is justified to disseminate Islam. (p. 319, Table 79)
23% young German Muslims are strongly antisemitic/anti-Christian (p.496.3rd paragraph)
France: 17% to 54% support for Sharia (2008)
(French poll)
http://www.csa.eu/multimedia/data/sondages/data2008/opi20080730-islam-et-citoyennete.htm
Question #2
"Islamic Law (Sharia) should be applied"
- fully, independently of the country of abode: 17%
- partly, adapted to the rules of the country of abode: 37%
- not at all in 'non-Muslim' countries: 38%