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Elon Musk clearly miscommunicated here. The Tesla is going to take awhile to cross Mars orbit. When will that be?

note: to future readers, the shape of the orbit shown in this tweet is no longer believed to be even close to correct. See answer(s) below for details on that.

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That map seems to be quite wrong now. See this answer and this comment and Jonathan McDowell's tweet.

Until there is a better resource for finding Roadster on the internet (and there is one coming! (mentioned here) I'll post this answer.

Using Horizons and a short Python script to plot it, I get the crossing about 154 days after 2018-Feb-08, or 2018-Jul-12. Coordinates are referenced to Roadster's projected position on JD=2458311.5. The thick red line is Mars' orbit and the thinner line is the Roadster projection, with dots at 145, 150, 155, and 160 days after 2018-Feb-08.

Note that the orbit in Horizons will probably be updated as more visual sightings are included, such as the one shown below.

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below: DEMIOS image from here as tweeted by Jonathan McDowell here. The little dot near the center moving to the right and up is Roadster in reflected sunlight, probably mostly from the white FH 2nd stage still attached.

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