In 2011, the World Health Organization  classified radio frequency radiation of the type used by WiFi devices as a Group 2B possible carcinogen. A study conducted by the University of Vienna have found WiFi exposures to cause genotoxicity as they break single and double strand DNAs in our body. This indicates that there are effects that may potentially surface with our future generations.
The advent of Wi-Fi connected high technology devices in executing day-to-day activities is fast evolving especially in developing countries of the world and hence the need to assess its safety among others. The present study was conducted to investigate the injurious effect of radiofrequency emissions from installed Wi-Fi devices in brains of young male rats. Animals were divided into four equal groups; group 1 served as control while groups 2, 3, and 4 were exposed to 2.5 Ghz at intervals of 30, 45, and 60 consecutive days with free access to food and water ad libitum. Alterations in harvested brain tissues were confirmed by histopathological analyses which showed vascular congestion and DNA damage in the brain was assayed using agarose gel electrophoresis. Histomorphometry analyses of their brain tissues showed perivascular congestion and tissue damage as well.
The present study was designed to investigate the possible DNA damaging effects of low-level microwave radiation (900, 1800, or 2450 MHz for 30 days) in brain of Fischer rats. Researchers demonstrated DNA damaging effects of low level microwave radiation in brain and concluded that low SAR microwave radiation exposure at these frequencies may induce DNA strand breaks in brain tissue.

There has been no rise in the rate of brain cancers despite a massive increase in the use of cell phones. If cell phones were causing cancer we could expect a significant rise in the rate of brain and other related cancers. According to the National Cancer Institute, there was no increase in the incidence of brain or other nervous system cancers between the years 1987 and 2005 despite the fact that cell phone use dramatically increased during those same years. [6] Between 2004 and 2010 there was still no significant change in the incidence rate of brain tumors. Between 2004 and 2010 there was a slight increase from 209 cases to 221.8 cases per 100,000 people, but this slight increase was attributed to better tracking and recording of cases. [43] During the same time period, cell phone use increased 62.7% from 182,140,362 subscribers in 2004 to 296,285,629 in 2010. [44]

The answer is yes, it can.  Will it always make people sick? No. Dr. George Carlo explains that there is most definitely a biological response to what he refers to as Information Carrying Radio Waves (ICRW-energy fields from many wireless devices).  When you're exposed to ICRW  a process of adaptation and compensation occurs in your body.  He has a great program that can help people adapt. 

In 2011, the International Agency for Research on Cancer (IARC), a component of the World Health Organization, appointed an expert Working Group to review all available evidence on the use of cell phones. The Working Group classified cell phone use as “possibly carcinogenic to humans,” based on limited evidence from human studies, limited evidence from studies of radiofrequency radiation and cancer in rodents, and inconsistent evidence from mechanistic studies (4).
These articles and websites don’t exist because the threat is real, however. They exist because they are a vehicle for turning people’s fear into money. The more people share nonsense articles about the dangers of Wi-Fi (or other harmless modern things) the more people click on them, the more ad-revenue is generated, and the more motivation the people peddling these rubbish articles have to keep creating and promoting them.
The most compelling evidence though comes from a Swedish team of cancer experts whose research stretches back 15 years. The results clearly demonstrate “a consistent association between long-term use of cell phone and cordless phones and glioma and acoustic neuroma”. Overall, they found that using a cell phone for more than a decade significantly increases the risk of a malignant tumour by almost two times with an analogue cell phone and by nearly four times with a digital phone. Interestingly, the risks were even higher for people who had started using mobiles as teenagers.