Robson-Kanu has not featured for the Championship side since suffering a thigh injury in the 1-1 draw with Cardiff on 19 March.
The 26-year-old featured in eight of Wales' qualifiers but injury ruled him out of the past four international friendlies.
"I'll be fit for the summer," he told BBC Wales Sport.
"I'm getting on well. No-one likes being injured, but it is just a little strain, so I am just managing it now and getting it right, and it will be right come the summer.
"I am definitely on the mend and looking forward to getting back fit."
Robson-Kanu, who is out of contract at the end of the season, expects to feature for Reading before the campaign finishes.
"I will hopefully play a few games and get my fitness up ahead of the camp and as we get ready for the summer," he said.
Wales have qualified their first major tournament since the 1958 World Cup in Sweden and will face Slovakia, England and Russia at the European Championship.
Robson-Kanu believes the success of Chris Coleman's team has helped to challenge the notion Wales is a rugby nation.
"Things have changed, there is this perception that Wales is a rugby nation and of course rugby is a massive part of this nation," he said.
"But if you look at the support Swansea and Cardiff get, especially when Cardiff were in the top league, it was fantastic.
"Now we are doing so well at international level, you can really feel the buzz and the attendances reflect that.
"We know how much it means to the fans, it is that special feeling isn't it? And that is what it is all about."
Robson-Kanu hopes to add to his tally of two international goals in France, and believes Wales can challenge in the tournament.
"What we've achieved getting there, great, but we want to do better than that," he said.
"We have players in the group who are programmed week in and week out to do better than that.
"It will be an exciting summer, but we want to be successful."

HBO tweeted the image with the message: "April #GoTSeason6 #GameOfThrones".
It is the first major hint since pictures of actor Kit Harington at an airport in Northern Ireland, where the series is filmed, went viral in July.
Snow was apparently murdered at the end of season five.
Fans last saw him lying stricken after he being brutally stabbed by his comrades in the Nights Watch.
Actress and Pitch Perfect 2 director Elizabeth Banks was one of thousands of fans who took to social media to question whether the character was really set to make a return.  She tweeted: "Fired up. Ready to go. #JonSnow".
Violeta Molina said: "Is he back for real? Is he a ghost? Is this all a cruel joke being played on us by HBO?"
Stage musician Ben Hanlin added: "You all thought he was dead.... You know nothing!"
Some fans are sceptical about the poster with Citizen D claiming: "Something feels off with that Jon snow poster. [I don't know] what kind of games HBO is playing but I don't like it one bit."
Scott Crawely took a slightly more hopeful look: "The real good news, If they can bring back Jon Snow they can bring back all of my other 30 favourite characters that died."
Channel 4 news anchor Jon Snow appeared to be slightly aggrieved his name was trending on social media, tweeting: "Winter is not coming: I have never been dead: I am a journalist: I am alarmed that my namesake has me trending!"
Game of Thrones, which began in 2011, has won 26 Primetime Emmy awards, including this year's outstanding drama series and a Bafta audience award in 2013.
Reading forward Hal Robson-Kanu says he will be fit for Wales' Euro 2016 campaign in France this summer.
[NEXT_CONCEPT]
A poster of a bloodied, but very much alive Jon Snow, has appeared to end months of speculation as to whether the popular Game of Thrones character will return in the sixth series.